CN107482673A - A kind of full distributed active distribution network economic load dispatching method of multizone - Google Patents
A kind of full distributed active distribution network economic load dispatching method of multizone Download PDFInfo
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- H02J3/383—
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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
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected 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
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
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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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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
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Abstract
The present invention proposes a kind of full distributed active distribution network economic load dispatching method of multizone, belongs to Operation of Electric Systems and control technology field, this method includes：1) establish and consider linearisation network loss and the minimum active distribution network economic load dispatching model for abandoning light cost；2) each region is realized by boundary node communication between neighbours：Newton matrix iteration initial value construction is intended in localization；Newton direction iterative calculation is intended in localization；Step-size in search is localized to calculate；3) global whether restrain judged by being communicated between neighbours after each region convergence.The inventive method is directed to active distribution network operation characteristic; make full use of point-to-point communication technology; based on full distributed quasi-Newton method; the full distributed superlinear convergence of multizone for completing active distribution network economic load dispatching calculates; without Consultation Center; reliability is improved, each region privacy is protected, realizes plug and play.
Description
Technical Field
The invention relates to an economic dispatching method for a multi-region fully-distributed active power distribution network, and belongs to the technical field of operation and control of power systems.
Background
With the increasing addition of distributed power sources, controllable loads, electric vehicles and other distributed resources to the power distribution network, the traditional passive power distribution network is changed into a more active form, and each user in the power distribution network is not only a consumer but also a production consumer, namely an active power distribution network. The new power distribution network form requires effective interaction between participants and the power grid, and can also consume distributed renewable energy sources and realize plug and play functions, so that the traditional centralized energy management mode is limited by the problems of increased computational burden and communication delay. Meanwhile, the power distribution side will present the situation of multi-benefit subjects (such as load aggregators) in the future, and the data of each subject will have valuable value, so the privacy protection problem is more prominent, and it is a very good solution idea to realize the collaborative optimization among multiple subsystems or areas through limited information communication among neighbors, but most of the mature algorithms nowadays only have linear or sub-linear convergence characteristics, the computing speed of a large system still needs to be improved, and it is very important to research the fully distributed optimization algorithm with the super-linear convergence property.
At present, a centralized or decomposition coordinated calculation method is mostly adopted for the power distribution network, because of the existence of a central controller, the central controller cannot meet the requirements of the future active power distribution network, and the traditional economic dispatching method can meet the bottlenecks of large calculation amount, high communication delay, poor information protection, low reliability and the like. It is a trend and necessity to develop a fully distributed approach that does not rely on a central controller based on point-to-point communication technology. Therefore, a new economic dispatching method of the active power distribution network with ultra-linear convergence and suitable for multiple areas needs to be researched.
Disclosure of Invention
The invention aims to provide a multi-region fully-distributed active power distribution network economic dispatching method, which overcomes the defects of the prior art, meets the aim of multi-region economic dispatching calculation of an active power distribution network by using a point-to-point communication technology and based on a fully-distributed quasi-Newton method, realizes that each region completes global optimization solution only through a small amount of information interaction between neighbors, can reduce the light abandon condition as far as possible, and maximizes the renewable energy utilization rate.
The invention provides an economic dispatching method for a multi-region fully-distributed active power distribution network, which comprises the following steps of:
(1) Establishing an economic dispatching model of the active power distribution network, which comprises the minimum light abandoning cost:
the objective function F of the economic dispatching model of the active power distribution network is as follows:
wherein T represents the total time of economic dispatching on the active power distribution network, T represents any time in the total time of economic dispatching, i is the ith distributed conventional small generator in the power distribution network,representing the collection of all distributed conventional small generators in the distribution network,representing a cost function of a conventional distributed small generator in a power distribution network, the cost function being calculated by the formula:wherein a is i 、b i And c i Respectively, the cost parameter, a, of the ith distributed conventional small generator in the power distribution network i 、b i And c i The values of (A) are respectively 0.01-1, 20-20.5 and 600-1500,the planned active power of the ith distributed conventional small generator in the power distribution network at the moment t, and j is the jth distribution in the power distribution networkFormula photovoltaic power generation equipmentRepresenting a collection of distributed photovoltaic power plants in a power distribution network, ω j The light abandoning penalty coefficient of the jth photovoltaic power generation equipment is 500-1000,representing the planned active power of the distributed photovoltaic power generation equipment in the power distribution network at time t,representing a predicted value of the distributed photovoltaic power generation equipment in the power distribution network at the time t;
the constraint conditions of the economic dispatching model of the active power distribution network comprise:
a) The load flow balance constraint condition considering the network loss of the active power distribution network is as follows:
wherein, the first and the second end of the pipe are connected with each other,the active power of the line between the node m and the node h in the power distribution network at the moment t,representing the active power of the line between node n and node m in the distribution network at time t,representing the active power loss of the line between node n and node m in the distribution network at time t, andrespectively representing historical data points of the active power and the reactive power of a line between a node n and a node m in the power distribution network and the voltage of the node n,andr is obtained from historical data of a power distribution network scheduling system mn Representing the line resistance between node n and node m in the distribution network,representing the active power output of node m in the distribution network at time t,
representing the active power of the generator at the time t of the node m in the distribution network,is a variable to be solved for the method,representing the load active power demand of a node m in the power distribution network at the time t;
centralizing variables to be solved in the power flow balance constraint condition considering the network loss of the active power distribution network, and rewriting the variables to be solved into the following matrix form:
B s x＝b
wherein, B s Representing an extended adjacency matrix, B s ＝[-Z B]Any element Z in the matrix Z op Comprises the following steps:
arbitrary element B in matrix B nu Comprises the following steps:
x represents the set of all variables to be solved, x is a vector,b represents the deviation of the active power of the nodes in the power distribution network, b is a vector,
b) The inequality constraint condition of the network where the active power distribution network is located is considered as follows:
the climbing constraint conditions of the conventional unit in the active power distribution network are as follows:
wherein, mu di And mu ii Respectively representing the climbing coefficient and the descending coefficient of the ith conventional unit in the power distribution network, wherein delta t is the set economic dispatching time interval of the power distribution network;
the constraint conditions of the active power of the conventional units in the active power distribution network are as follows:
wherein the content of the first and second substances,andrespectively representing the upper limit of active power of the ith conventional unit in the power distribution networkAnd an active power lower limit;
the constraint conditions of the line tide capacity in the active power distribution network are as follows:
wherein, the first and the second end of the pipe are connected with each other,andrepresenting the upper limit/the lower limit of active power of a line power flow between a node n and a node m in the power distribution network;
the active power constraint conditions of the photovoltaic units in the active power distribution network are as follows:
writing inequality constraint conditions of the network where the active power distribution network is located into a matrix form as follows:
(2) And (3) converting the economic dispatching model of the active power distribution network into the following KKT condition equation by adopting a primal-dual interior point method:
wherein r is pri Is the original residual of the KKT conditional equation, r dual And r cent The dual residual and the central residual of the KKT conditional equation, respectively, dq represents the function gradient matrix,λ and ν are respectively the above-mentioned inequalitiesDual multipliers of formula (la) and equality-constrained, gamma is a calculation parameter,mu is a factor, the value of g is 10, and the value of g is equal to twice of the total number Y of the inequality constraint conditions;
solving the KKT conditional equation by using a numerical iteration method, defining y = (x, λ, v) and Δ y = ([ delta ] x, [ delta ] λ, and Δ v), and then the iterative solution formula of the KKT conditional equation is:
y k+1 ＝y k +d k △y k
wherein k is the number of iterations, y k Represents the value of y at the kth iteration, d k Represents the value of step length at the kth iteration,. DELTA.y k Representing the search direction at the k-th iteration;
obtaining the search direction delta y according to a first-order Taylor expansion formula by using the following formula k ：
△y k ＝-(Dr γ (y k )) -1 r γ (y k )
Wherein, the first and the second end of the pipe are connected with each other, representing a quadratic gradient calculation, superscript T Representing matrix transposition, diag representing an operation on a diagonal matrix, B s Represents an extended adjacency matrix;
(3) Solving y in the KKT conditional equation to realize economic dispatching of the multi-region fully-distributed active power distribution network, firstly defining the connection lines between the regions in the active power distribution network as follows: the method comprises the following steps of performing region allocation on the links between regions in the active power distribution network, wherein the links between any two regions belong to the region with the smaller number of nodes:
(3-1) setting an economic dispatching initial time t =0 during initialization;
(3-2) setting the initial iteration step number k =0 of the active power distribution network multi-region fully-distributed economic scheduling calculation at the time t;
(3-3) solving the approximation matrix H, comprising the steps of:
(3-3-1) constructing an approximate matrix initial value H of a region N in an active power distribution network N (0)：
H N (0)＝M N +L N
Wherein M is N Is a block diagonal matrix comprising an area N and other areas connected to the area N, each diagonal block in the block diagonal matrix being defined by the Dr of each area in the distribution network γ (y 0 ) Namely Dr γ Initial value composition of (y), L N Is a non-block diagonal symmetric matrix, the elements in the non-block diagonal symmetric matrix are formed by the initial value H of an approximate matrix N (0) The element composition in the B matrix of the corresponding position;
(3-3-2) dual residual errors and original residual errors r in KKT conditional equation of region N in active power distribution network dual And r pri The local dual residual r after correction is obtained by respectively correcting dualN And the original residual r priN ：
Wherein, subscript N indicates that the element is an element in an area N in the active power distribution network, and vector M rdualN Any element in (1) is M rdualN (p N +n)，
Region Q is connected to region N, p N Is the number of generators in the N region, vector M rpriN Any element in (1) is M rpriN (n)，
p Q Is the number of generators in the Q region, la NQ Is the above B s The values of the boundary elements at the junction of region N and region Q in the matrix,N n and Q m Respectively representing a boundary node N of an area N in the power distribution network and a boundary node m of an area Q connected with the area N;
(3-3-3) obtaining an area N approximate matrix H in the power distribution network of the (k + 1) th iteration by utilizing a quasi-Newton method and calculating according to the following formula N (k+1)：
Wherein, the first and the second end of the pipe are connected with each other,tau is an adjustment parameter and takes a value of 10 -3 I is an identity matrix, subscript nN Representing the extension variables of boundary nodes and corresponding lines which comprise an area N and an area connected with the area N in the power distribution network;
(3-4) calculating the extended search direction of the area N in the power distribution network by using the approximate matrix H obtained in the step (3-3) according to the following formula:
wherein gamma is an adjustment parameter with a value of 10 -4 ，The extension variables representing the k-th iteration including the region N and the boundary nodes of the regions connected to the region N in the distribution network and the corresponding lines, the active power variables of the generators representing the region N and the boundary nodes of the regions connected with the region N in the power distribution network and the active power variable of the power flow of the corresponding lines,andrespectively representing the dual variables of an area N, an area boundary node connected with the area N and a corresponding line in the power distribution network;
(3-5) Using the extended search Direction obtained in the above step (3-4)The search direction for region N is calculated using the following equation:
wherein, w N Representing the total number of regions including region N and the regions contiguous to region N,the search direction of the variable in the area N corresponding to the expanded search direction of the distribution network area f in the k iteration is obtained;
(3-6) calculating the step length in the iterative solution formula of the KKT conditional equation of the region N in the power distribution network by using the following formulaThe method comprises the following steps:
(3-6-1) respectively calculating first middle step lengths of all areas in the power distribution network, wherein the first middle step length of the area N is recorded as
(3-6-2) exchanging the calculated first intermediate step length between all the areas and all the other connected areas;
(3-6-3) taking region N as an example, region N receives the first intermediate step size of all other connected regions, and calculates the second intermediate step size of region N by using the following formula
(3-6-4) according to the second intermediate stepRegion N calculating search step size for region N Using formulasFor search step lengthUpdating and utilizing according to the updated search step lengthUpdatingUsing updatedCalculating q (y) k+1 ) Up to q (y) k+1 )≤0；
(3-6-5) according to the search step sizeUsing formulasFor the search step lengthUpdating and utilizing according to the updated search step lengthUpdatingUsing updatedCalculate | | | r γ (y N k+1 )|| 2 Up toExchange with connected areaAnd updating the search step size Wherein, alpha and beta are backtracking parameters with the values of 0.01 to 0.1 and 0.3 to 0.8;
(3-6-6) search variable Deltay according to the region N N k And search step d of region N N k Solution of the above KKT conditional equation y N k And (3) updating:
y N k+1 ＝y N k +d N k △y N k ；
(3-7) calculating residual total r of the region N in the power distribution network feas And proxy gap Setting a threshold value epsilon for convergence of iterative calculation of a region feas According to a threshold value epsilon feas Determining whether the region iteration calculation converges, where feas Value of 10 -8 ～10 -6 ；
(3-8) based on the total residual r feas And proxy gapSolution y to the above KKT conditional equation N k Is judged if r is the convergence state of feas ≤ε feas And is andsolution y of the KKT conditional equation for region N in the distribution network N k Converging, setting a region N convergence flag Conv in the distribution network N =1, go to step (3-9), if r feas >ε feas Andone or both of them are satisfied, then the region N convergence flag Conv is asserted N Go to step (3-3-2) with =0,k = k + 1;
(3-9) Conv according to the local convergence status N And (3) performing global convergence state calculation:
the communication exchange local convergence state of the defined region N and the connected region is calculated as a global convergence mark:
(3-10) if the global convergence flag1, completing economic dispatching solution of the multi-region fully-distributed active power distribution network at the time t to obtain planned active power of each conventional generator in the power distribution network at the time tAnd planned active power of the photovoltaic power generation plantWhile setting t = t +1 to go (3-11), ifEnabling k = k +1, turning to the step (3-3-2), and continuing to perform next iterative calculation;
(3-11) if T = T, finishing the calculation to obtain the planned active power of each conventional generator in the power distribution network at each moment T in the T timeAnd planned active power of the photovoltaic power generation plantCompleting economic dispatch of the multi-region fully-distributed active power distribution network if t&And (T), going to the step (3-2).
The economic dispatching method for the multi-region fully-distributed active power distribution network provided by the invention has the advantages that:
the economic dispatching method of the multi-region fully-distributed active power distribution network provided by the invention has the advantages that renewable energy sources can be utilized to the maximum extent in the multi-region economic dispatching of the active power distribution network, the light loss is greatly reduced, meanwhile, the economic dispatching method has the characteristics of high calculation efficiency and high convergence speed, and because a central controller does not exist, each region only exchanges limited boundary information by using a point-to-point communication technology, the communication traffic is small, the time delay is low, the privacy information is protected, the requirement of plug-and-play characteristics can be met, and in addition, the accurate dispatching can be realized under the condition of asynchronous communication or communication failure. In conclusion, the method and the device can play an important role in multi-area economic dispatching of the active power distribution network.
Drawings
Fig. 1 is a schematic diagram of an active power distribution network economic dispatching method according to the present invention, in which a region is divided into three regions.
Fig. 2 is a block diagram of a calculation process of economic dispatch of a multi-zone fully-distributed active power distribution network according to the present invention.
Fig. 3 is an exemplary schematic diagram of two regions for calculating an initial value of a KKT matrix according to the method of the present invention.
FIG. 4 is a schematic diagram illustrating two exemplary areas of search direction calculation information interaction according to the method of the present invention.
Detailed Description
The economic dispatching method for the multi-region fully-distributed active power distribution network, provided by the invention, considers an economic dispatching model of maximum renewable energy consumption and a fully-distributed multi-region optimization solving method. The fully-distributed multi-region optimization solving method completes the global optimization solving process through communication between neighbor regions, does not need a global central controller, is based on a quasi-Newton method with super-linear convergence, and can adapt to asynchronous communication conditions to a certain degree, and comprises the following steps:
(1) Establishing an economic dispatching model of the active power distribution network, which comprises the minimum light abandoning cost:
the objective function F of the economic dispatching model of the active power distribution network is as follows:
wherein T represents the input to the active distribution networkThe total time of economic dispatch is passed, t represents any time in the total time of economic dispatch, i is the ith distributed conventional small generator in the power distribution network,representing the collection of all distributed conventional small generators in the distribution grid,representing a cost function of a conventional distributed small generator in a power distribution network, the cost function being calculated by the formula:wherein a is i 、b i And c i Respectively a cost parameter of the ith distributed conventional small generator in the power distribution network, a i 、b i And c i The values of (a) are respectively 0.01-1, 20-20.5 and 600-1500, in one embodiment of the invention, a i 、b i And c i Are respectively 0.05, 20.3 and 800,j is the jth distributed photovoltaic power generation equipment (also can be distributed renewable energy generators in the power distribution network such as a small wind driven generator) in the power distribution network,representing a collection of distributed photovoltaic power plants in a power distribution network, omega j The light abandoning penalty coefficient of the jth photovoltaic power generation equipment is 500-1000, and in one embodiment of the invention, omega is j The value of (a) is 600,representing the planned active power of the distributed photovoltaic power generation equipment in the power distribution network at the time t, is a variable to be solved by the method,representing a predicted value of the distributed photovoltaic power generation equipment in the power distribution network at the time t;
the constraint conditions of the economic dispatching model of the active power distribution network comprise:
a) The load flow balance constraint condition considering the network loss of the active power distribution network is as follows:
wherein the content of the first and second substances,the active power of the line between the node m and the node h in the power distribution network at the time t,representing the active power of the line between node n and node m in the distribution network at time t,is a variable to be solved for the method,representing the active power loss of the line between node n and node m in the distribution network at time t,
andrespectively representing historical data points of the active power and the reactive power of a line between a node n and a node m in the power distribution network and the voltage of the node n,andr is obtained from historical data of a power distribution network scheduling system mn Representing the line resistance between node n and node m in the distribution network,representing the active power output of node m in the distribution network at time t, representing the active power of the generator at the node m in the distribution network at the moment t,is a variable to be solved for the method,representing the load active power demand of a node m in the power distribution network at the time t;
centralizing variables to be solved in the power flow balance constraint condition considering the network loss of the active power distribution network, and rewriting the variables to be solved into the following matrix form:
B s x＝b
wherein, B s Representing an extended adjacency matrix, B s ＝[-Z B]Any element Z in the matrix Z op Comprises the following steps:
arbitrary element B in matrix B nu Comprises the following steps:
x represents the set of all variables to be solved, x is a vector,b represents the deviation of the active power of the nodes in the power distribution network, b is a vector,
b) The inequality constraint condition of the network where the active power distribution network is located is considered as follows:
the climbing constraint conditions of the conventional unit in the active power distribution network are as follows:
wherein, mu di And mu ii Respectively representing the climbing coefficient and the descending coefficient of the ith conventional unit in the power distribution network, wherein delta t is the set economic dispatching time interval of the power distribution network;
the constraint conditions of the active power of the conventional unit in the active power distribution network are as follows:
wherein the content of the first and second substances,andrespectively representing the upper limit of active power and the lower limit of active power of the ith conventional unit in the power distribution network;
the constraint conditions of the line tide capacity in the active power distribution network are as follows:
wherein the content of the first and second substances,andrepresenting the upper limit/the lower limit of active power of a line power flow between a node n and a node m in the power distribution network;
the active power constraint conditions of the photovoltaic units in the active power distribution network are as follows:
writing inequality constraint conditions of the network where the active power distribution network is located into a matrix form as follows:
(2) And (3) converting the economic dispatching model of the active power distribution network into a KKT (Karush-Kuhn-Tucker) condition equation as follows by adopting a primal-dual interior point method:
wherein r is pri Is the original residual of the KKT conditional equation, r dual And r cent Dual residual and central residual of the KKT conditional equation, respectively, dq represents a function gradient matrix,λ and ν are the dual multipliers of the above inequalities and equality constraints, respectively, γ is a calculation parameter,mu is a factor, the value of g is 10, and the value of g is equal to twice of the total number Y of the inequality constraint conditions;
solving the KKT conditional equation by using a numerical iteration method, defining y = (x, λ, v) and Δ y = ([ delta ] x, [ delta ] λ, and Δ v), and then the iterative solution formula of the KKT conditional equation is:
y k+1 ＝y k +d k △y k
wherein k is the number of iterations, y k Represents the value of y at the k iteration, d k Represents the value of step length at the kth iteration,. DELTA.y k Representing the search direction at the k-th iteration;
obtaining the search direction delta y according to a first-order Taylor expansion formula by using the following formula k ：
△y k ＝-(Dr γ (y k )) -1 r γ (y k )
Wherein the content of the first and second substances, representing a quadratic gradient calculation, superscript T Representing matrix transposition, diag representing an operation on a diagonal matrix, B s Represents an extended adjacency matrix;
(3) Solving y in the KKT conditional equation to realize economic dispatching of the multi-region fully-distributed active power distribution network, and firstly defining the connection line between regions in the active power distribution network as follows: area allocation is carried out on the links between areas in the active power distribution network, the links between any two areas belong to the area with the smaller number of nodes, as shown in fig. 1, nodes n, m and h in the power distribution network respectively belong to the area A, B, C and h<n&M, the region A passes through the connecting line l nm ，l nh Connecting to the region B and the region C, the connecting line l nm Belonging to the area A, the tie line l nh Belonging to the region C. Comprising the following steps, as shown in fig. 2:
(3-1) setting an economic dispatching initial time t =0 during initialization;
(3-2) setting the initial iteration step number k =0 of the active power distribution network multi-region fully-distributed economic scheduling calculation at the time t;
(3-3) solving the approximation matrix H, comprising the steps of:
due to (Dr) γ (y)) -1 Direct full-distributed multi-area solution cannot be realized, and an approximate matrix H needs to be searched to replace Dr γ And (y), finally solving the KKT condition equation.
(3-3-1) constructing an approximate matrix initial value H of a region N in an active power distribution network N (0)：
The construction of an initial value matrix can be completed only through information interaction with a boundary node of a neighbor region, and the initial value H of an approximate matrix of a region N N (0) The device consists of two parts:
H N (0)＝M N +L N
wherein M is N Is a block diagonal matrix comprising an area N and other areas connected to the area N, each diagonal block in the block diagonal matrix being defined by the Dr of each area in the distribution network γ (y 0 ) Namely Dr γ (y) initial value composition, L N Is a non-block diagonal symmetric matrix, the elements in the non-block diagonal symmetric matrix are formed by the initial value H of an approximate matrix N (0) The element composition in the B matrix of the corresponding position; as shown in fig. 3, for two regions H N (0) As an example of the initial value,A int respectively representing a boundary node n of an A area and an internal node of the A area in the power distribution network,representing a boundary node m in the distribution network,
(3-3-2) due to B s Presence of a network coupling element, r pri r dual Realizing the residual localization calculation needs to realize certain correction with the information communication of the neighboring boundary region, r cent No correction is required.
Dual residual and original residual r in KKT conditional equation of region N in active power distribution network dual And r pri The local dual residual r after correction is obtained by respectively correcting dualN And the original residual r priN ：
Wherein, subscript N indicates that the element is an element in an area N in the active power distribution network, and vector M rdualN Any element in (1) is M rdualN (p N +n)，
Region Q is connected to region N, p N Is the number of generators in the N region, vector M rpriN Any element in (1) is M rpriN (n)，
p Q Is the number of generators in the Q region, la NQ Is the above B s The values of the boundary elements at the junction of region N and region Q in the matrix,N n and Q m Respectively representing a boundary node N of an area N and a boundary node m of an area Q connected with the area N in the power distribution network;
(3-3-3) obtaining a region N approximate matrix H in the power distribution network of the (k + 1) th iteration by utilizing a quasi-Newton method and calculating through the following formula N (k+1)：
Wherein, the first and the second end of the pipe are connected with each other,tau is an adjustment parameter and takes the value of 10 -3 And I is an identity matrix, and compared with a traditional quasi-Newton method formula, the above formula can ensure the positive nature of an approximate matrix, thereby ensuring the convergence of the algorithm. Subscript nN Representing the extension variables of boundary nodes and corresponding lines which comprise an area N and an area connected with the area N in the power distribution network;
(3-4) calculating the extended search direction of the area N in the power distribution network by using the approximate matrix H obtained in the step (3-3) according to the following formula:
wherein gamma is an adjustment parameter with a value of 10 -4 ，The extension variables representing the k-th iteration including the region N and the boundary nodes of the regions connected to the region N in the distribution network and the corresponding lines, the active power variables of the generators representing the region N and the boundary nodes of the regions connected with the region N in the power distribution network and the active power variable of the power flow of the corresponding lines,andrespectively representing the dual variables of an area N, an area boundary node connected with the area N and a corresponding line in the power distribution network;
(3-5) Using the extended search Direction obtained in the above step (3-4)The search direction for region N is calculated using the following equation:
acquiring a corresponding local area partial value of the neighbor area extended search direction by utilizing communication, and simultaneously transmitting corresponding information to the neighbor area to realize the reassembly of the search direction, wherein finally the search direction of the N area can be obtained by the following formula:
wherein, w N Representing the total number of regions including region N and the regions contiguous to region N,the search direction of the variables in the area N corresponding to the extended search direction of the distribution network area f in the kth iteration is shown as an information interaction diagram of two areas AB in the distribution network in fig. 4, where the two areas AB only need to be exchangedAnd withRespectively representing a B area boundary variable part contained in the calculation of the A area expansion direction and an A area boundary variable part contained in the calculation of the B area expansion direction, wherein the rest variables are area internal interaction variables and do not need to communicate with the outside;
(3-6) calculating the step length in the iterative solution formula of the KKT conditional equation of the region N in the power distribution network by using the following formulaThe method comprises the following steps:
the step length is calculated by adopting the following fully distributed backtracking search mode:
(3-6-1) respectively calculating first middle step lengths of all areas in the power distribution network, wherein the first middle step length of the area N is recorded as
(3-6-2) exchanging the calculated first intermediate step length between all the areas and all the other connected areas;
(3-6-3) taking region N as an example, region N receives the first intermediate step size of all other connected regions, and calculates the second intermediate step size of region N by using the following formula
(3-6-4) according to the second intermediate step sizeRegion N calculates search step size for region N Using a formulaFor search step lengthUpdating and utilizing according to the updated search step lengthUpdatingUsing updatedCalculating q (y) k+1 ) Up to q (y) k+1 )≤0；
(3-6-5) according to the search step sizeUsing formulasFor search step lengthUpdating and utilizing according to the updated search step lengthUpdatingUsing updatedCalculate | | | r γ (y N k+1 )|| 2 Up toExchange with connected areaAnd updating the search step size Wherein, alpha and beta are backtracking parameters with the values of 0.01 to 0.1 and 0.3 to 0.8; in one embodiment of the invention, the values of α and β are 0.05 and 0.4, respectively;
(3-6-6) search variable Deltay according to the region N N k And search step d of region N N k Solution of the above KKT conditional equation y N k Updating:
y N k+1 ＝y N k +d N k △y N k ；
(3-7) calculating residual total r of the region N in the power distribution network feas And proxy gap Setting a threshold value epsilon for convergence of iterative calculation of a region feas According to a threshold value epsilon feas Determining whether the region iteration calculation converges, where feas Value of 10 -8 ～10 -6 In one embodiment of the invention,. Epsilon. feas Is taken as value of 10 -6 ；
(3-8) based on the total residual r feas And proxy gapSolution y to the above KKT conditional equation N k Is judged if r is the convergence state of feas ≤ε feas And is andsolution y of KKT conditional equation for region N in the distribution network N k Converging, setting a region N convergence flag Conv in the distribution network N If r is not less than 1, go to step (3-9) feas >ε feas And withOne or both of them are satisfied, then the region N convergence flag Conv is asserted N Go to step (3-3-2) with =0,k = k + 1;
(3-9) Conv according to the local convergence status N And (3) performing global convergence state calculation:
the communication exchange local convergence state of the defined region N and the connected region is calculated as a global convergence mark:
(3-10) if the global convergence flag1, completing economic dispatching solution of the multi-region fully-distributed active power distribution network at the time t to obtain planned active power of each conventional generator in the power distribution network at the time tAnd planned active power of the photovoltaic power generation plantWhile setting t = t +1 to go to (3-11), ifEnabling k = k +1, turning to the step (3-3-2), and continuing to perform next iterative calculation;
(3-11) if T = T, finishing the calculation to obtain the planned active power of each conventional generator in the power distribution network at each moment T in the T timeAnd planned active power of the photovoltaic power generation equipmentCompleting economic dispatch of the multi-region fully-distributed active power distribution network if t&And (T), going to the step (3-2).
Claims (1)
1. A multi-region full-distributed active power distribution network economic dispatching method is characterized by mainly comprising the following steps:
(1) Establishing an economic dispatching model of the active power distribution network, which comprises the minimum light abandoning cost:
the objective function F of the economic dispatching model of the active power distribution network is as follows:
wherein T represents the total time of economic dispatching on the active power distribution network, T represents any time in the total time of economic dispatching, i is the ith distributed conventional small generator in the power distribution network,representing the collection of all distributed conventional small generators in the distribution grid,representing a cost function of a conventional distributed small generator in a power distribution network, the cost function being calculated by the formula:wherein a is i 、b i And c i Respectively a cost parameter of the ith distributed conventional small generator in the power distribution network, a i 、b i And c i The values of (A) are respectively 0.01-1, 20-20.5 and 600-1500,the planned active power of the ith distributed conventional small generator in the power distribution network at the moment t, and j is the jth distributed photovoltaic power generation equipment in the power distribution networkRepresenting a collection of distributed photovoltaic power plants in a power distribution network, omega j The light abandoning penalty coefficient of the jth photovoltaic power generation equipment is 500-1000,representing the planned active power of the distributed photovoltaic power generation equipment in the power distribution network at time t,representing a predicted value of the distributed photovoltaic power generation equipment in the power distribution network at the time t;
the constraint conditions of the economic dispatching model of the active power distribution network comprise:
a) The load flow balance constraint condition considering the network loss of the active power distribution network is as follows:
wherein the content of the first and second substances,the active power of the line between the node m and the node h in the power distribution network at the moment t,representing the active power of the line between node n and node m in the distribution network at time t,representing the active power loss of the line between node n and node m in the distribution network at time t, andrespectively representing historical data points of the active power and the reactive power of a line between a node n and a node m in the power distribution network and the voltage of the node n,andobtaining r from historical data of a power distribution network dispatching system mn Representing the line resistance between node n and node m in the distribution network,representing the active power output of node m in the distribution network at time t, representing the active power of the generator at the node m in the distribution network at the moment t,is a variable to be solved for the method,representing the load active power demand of a node m in the power distribution network at the time t;
centralizing variables to be solved in the power flow balance constraint condition considering the network loss of the active power distribution network, and rewriting the variables to be solved into the following matrix form:
B s x＝b
wherein, B s Representing an extended adjacency matrix, B s ＝[-Z B]Any element Z in the matrix Z op Comprises the following steps:arbitrary element B in matrix B nu Comprises the following steps:x represents all variables to be claimedA set of quantities, x being a vector,b represents the deviation of the active power of the nodes in the power distribution network, b is a vector,
b) The inequality constraint condition of the network where the active power distribution network is located is considered as follows:
the climbing constraint conditions of the conventional unit in the active power distribution network are as follows:
wherein, mu di And mu ii Respectively representing the climbing coefficient and the descending coefficient of the ith conventional unit in the power distribution network, wherein delta t is the set economic dispatching time interval of the power distribution network;
the constraint conditions of the active power of the conventional units in the active power distribution network are as follows:
wherein the content of the first and second substances,andrespectively representing the upper limit of active power and the lower limit of active power of the ith conventional unit in the power distribution network;
the constraint conditions of the line tide capacity in the active power distribution network are as follows:
wherein the content of the first and second substances,andrepresenting the upper limit/the lower limit of active power of a line power flow between a node n and a node m in the power distribution network;
the active power constraint conditions of the photovoltaic units in the active power distribution network are as follows:
writing inequality constraint conditions of the network where the active power distribution network is located into a matrix form as follows:
(2) And (3) converting the economic dispatching model of the active power distribution network into the following KKT condition equation by adopting a primal-dual interior point method:
2
wherein r is pri Is the original residual of the KKT conditional equation, r dual And r cent The dual residual and the central residual of the KKT conditional equation, respectively, dq represents the function gradient matrix,λ and ν are the dual multipliers of the above inequalities and equality constraints, respectively, γ is a calculation parameter,mu is a factor, the value of g is 10, and the value of g is equal to twice of the total number Y of the inequality constraint conditions;
solving the KKT conditional equations by using a numerical iteration method, which defines y = (x, λ, v), Δ y = (Δ x, Δ λ, Δ v), and then the iterative solution formula of the KKT conditional equations is:
y k+1 ＝y k +d k Δy k
where k is the number of iterations, y k Represents the value of y at the k iteration, d k Represents the value of the step length at the kth iteration, Δ y k Representing the search direction at the kth iteration;
according to a first-order Taylor expansion formula, the searching direction delta y is obtained by using the following formula k ：
Δy k ＝-(Dr γ (y k )) -1 r γ (y k )
Wherein the content of the first and second substances, representing a quadratic gradient calculation, superscript T Representing a matrix transposition, diag representing an operation of taking a diagonal matrix, B s Represents an extended adjacency matrix;
(3) Solving y in the KKT conditional equation to realize economic dispatching of the multi-region fully-distributed active power distribution network, firstly defining the connection lines between the regions in the active power distribution network as follows: the method comprises the following steps of performing region allocation on the links between regions in the active power distribution network, wherein the links between any two regions belong to the region with the smaller number of nodes, and the method comprises the following steps:
(3-1) setting an economic dispatching initial time t =0 during initialization;
(3-2) setting the initial iteration step number k =0 of the active power distribution network multi-region fully-distributed economic scheduling calculation at the time t;
(3-3) solving the approximation matrix H, comprising the steps of:
(3-3-1) constructing an approximate matrix initial value H of a region N in an active power distribution network N (0)：
H N (0)＝M N +L N
Wherein M is N Is a block diagonal matrix comprising an area N and other areas connected to the area N, each diagonal block in the block diagonal matrix being defined by the Dr of each area in the distribution network γ (y 0 ) Namely Dr γ Initial value composition of (y), L N Is a non-block diagonal symmetric matrix, the elements in the non-block diagonal symmetric matrix are formed by the initial value H of an approximate matrix N (0) The element composition in the B matrix of the corresponding position; (ii) a
(3-3-2) dual residual errors and original residual errors r in KKT conditional equations of region N in active power distribution network dual And r pri The local dual residual r after correction is obtained by respectively correcting dualN And the original residual r priN ：
Wherein, subscript N indicates that the element is an element in an area N in the active power distribution network, and vector M rdualN Any element in (1) is M rdualN (p N +n)，Region Q is connected to region N, p N Is the number of generators in the N region, vector M rpriN Any element in (1) is M rpriN (n)，p Q Is the number of generators in the Q region, la NQ Is the above B s The values of the boundary elements at the junction of region N and region Q in the matrix,N n and Q m Respectively representing a boundary node N of an area N and a boundary node m of an area Q connected with the area N in the power distribution network;
(3-3-3) obtaining an area N approximate matrix H in the power distribution network of the (k + 1) th iteration by utilizing a quasi-Newton method and calculating according to the following formula N (k+1)：
Wherein the content of the first and second substances,tau is an adjustment parameter and takes the value of 10 -3 I is an identity matrix, subscript n N Representing the extension variables of boundary nodes and corresponding lines which comprise an area N and an area connected with the area N in the power distribution network;
(3-4) calculating the extended search direction of the area N in the power distribution network by using the approximate matrix H obtained in the step (3-3) according to the following formula:
wherein gamma is an adjustment parameter with a value of 10 -4 ，The extension variables representing the k-th iteration including the region N and the boundary nodes of the regions connected to the region N in the distribution network and the corresponding lines, the active power variables of the generators representing the region N and the boundary nodes of the regions connected with the region N in the power distribution network and the active power variable of the power flow of the corresponding lines,andrespectively representing the dual variables of an area N, an area boundary node connected with the area N and a corresponding line in the power distribution network;
(3-5) Using the extended search Direction obtained in the above step (3-4)The search direction for region N is calculated using the following equation:
wherein, w N Representing the total number of regions including region N and the regions contiguous to region N,the search direction of the variable in the area N corresponding to the expanded search direction of the distribution network area f in the k iteration is obtained;
(3-6) calculating the step length in the iterative solution formula of the KKT conditional equation of the region N in the power distribution network by using the following formulaThe method comprises the following steps:
(3-6-1) respectively calculating first middle step lengths of all areas in the power distribution network, wherein the first middle step length of the area N is recorded as
(3-6-2) exchanging the calculated first intermediate step length between all the areas and all the other connected areas;
(3-6-3) taking region N as an example, region N receives the first intermediate step size of all other connected regions, and calculates the second intermediate step size of region N by using the following formula
(3-6-4) according to the second intermediate step sizeRegion N calculates search step size for region N Using formulasFor search step lengthUpdating and utilizing according to the updated search step lengthUpdatingUsing updatedCalculating q (y) k+1 ) Up to q (y) k+1 )≤0；
(3-6-5) according to the search step sizeUsing formulasFor search step lengthUpdating and utilizing according to the updated search step lengthUpdatingUsing updatedCalculate | | | r γ (y N k+1 )|| 2 Up toExchange with connected areaAnd updating the search step size Wherein, alpha and beta are backtracking parameters with the values of 0.01 to 0.1 and 0.3 to 0.8;
(3-6-6) search variable Deltay according to the above region N N k And search step d of region N N k Solution of the above KKT conditional equation y N k Updating:
y N k+1 ＝y N k +d N k Δy N k ；
(3-7) calculating the residue of the region N in the distribution networkTotal amount of difference r feas And proxy gap Setting a threshold value epsilon for convergence of iterative calculation of a region feas According to a threshold value epsilon feas Determining whether the region iteration calculation converges, where feas Value of 10 -8 ～10 -6 ；
(3-8) based on the total amount of the residual r feas And proxy gapSolution y to the above KKT conditional equation N k Is judged if r is the convergence state of feas ≤ε feas And is made ofSolution y of the KKT conditional equation for region N in the distribution network N k Convergence, setting region N convergence flag Conv in distribution network N If r is not less than 1, go to step (3-9) feas >ε feas Andone or both of them are satisfied, then the region N convergence flag Conv is asserted N Go to step (3-3-2) with =0,k = k + 1;
(3-9) Conv according to the local convergence status N And (3) performing global convergence state calculation:
the communication exchange local convergence state of the defined region N and the connected region is calculated as a global convergence mark:
(3-10) if the global convergence flag1, completing economic dispatching solving of the multi-region fully-distributed active power distribution network at the time t to obtain planned active power of each conventional generator in the power distribution network at the time tAnd planned active power of the photovoltaic power generation plantWhile setting t = t +1 to go (3-11), ifEnabling k = k +1, turning to the step (3-3-2), and continuing to perform next iterative calculation;
(3-11) if T = T, finishing the calculation to obtain the planned active power of each conventional generator in the power distribution network at each moment T in the T timeAnd planned active power of the photovoltaic power generation equipmentCompleting economic dispatch of the multi-region fully-distributed active power distribution network if t&And (T), going to the step (3-2).
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