CN116826722A - ADMM-based distributed photovoltaic maximum access capacity evaluation method and system - Google Patents
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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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- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract
The application belongs to the technical field of power distribution network optimization operation, and discloses a distributed photovoltaic maximum access capacity assessment method and system based on ADMM; the method comprises the following steps: step 1, based on power distribution network subareas, acquiring a subarea-based distributed photovoltaic maximum access capacity evaluation model; and 2, carrying out distributed solution on the partition-based distributed photovoltaic maximum access capacity evaluation model based on a synchronous ADMM algorithm to obtain a distributed photovoltaic optimal access strategy. The application establishes the maximum access capacity evaluation model of the distributed photovoltaic, adopts the synchronous ADMM algorithm to carry out distributed solution on the model, and can obtain the optimal access strategy of the distributed photovoltaic.
Description
Technical Field
The application belongs to the technical field of power distribution network optimization operation, and particularly relates to a distributed photovoltaic maximum access capacity assessment method and system based on ADMM.
Background
Under the background of carbon reduction, the great development of clean energy represented by wind power and photovoltaic has become the consensus of the energy and power industry; in recent years, distributed photovoltaic development is continually jumping on new steps.
The relevant specialists indicate that distributed photovoltaic is the best mode for solar photovoltaic power generation applications. The distributed photovoltaic system is a photovoltaic power generation facility which is built nearby a user site and is characterized by balance adjustment of a power distribution system, and has the characteristics of being suitable for local conditions, clean, efficient, distributed, near-to-near and the like.
Along with the continuous improvement of the permeability of the distributed photovoltaic in the power distribution network, a series of phenomena such as power flow foldback and voltage out-of-limit are brought to the power distribution network, and photovoltaic batch off-grid can be caused under extreme conditions, so that the safe and stable operation of the power grid is seriously threatened. Therefore, it is necessary to evaluate the maximum capacity of the distribution network that allows access to the distributed photovoltaic.
Disclosure of Invention
The present application is directed to a method and a system for evaluating maximum access capacity of a distributed photovoltaic based on ADMM, so as to solve one or more of the above-mentioned technical problems.
In order to achieve the above purpose, the application adopts the following technical scheme:
the application provides an ADMM-based distributed photovoltaic maximum access capacity assessment method, which comprises the following steps:
step 1, based on power distribution network subareas, acquiring a subarea-based distributed photovoltaic maximum access capacity evaluation model;
and 2, carrying out distributed solution on the partition-based distributed photovoltaic maximum access capacity evaluation model based on a synchronous ADMM algorithm to obtain a distributed photovoltaic optimal access strategy.
The method is further improved in that the step 1 specifically comprises the following steps:
acquiring a photovoltaic maximum access capacity evaluation original model of a power distribution network system;
carrying out convexity on a photovoltaic maximum access capacity evaluation original model of the power distribution network system to obtain a convex quadratic programming model;
establishing a partition-based distributed photovoltaic maximum access capacity assessment model based on a power distribution network system partition and a convex quadratic programming model;
wherein, the objective function of the photovoltaic maximum access capacity evaluation original model of the power distribution network system is that,
F＝α 1 F PV +α 2 F loss ；
in the formula ,α1 、α 2 Is a weight coefficient; f (F) PV 、F loss Respectively standardized distributed photovoltaic access capacity and active power loss of a network;
the constraint conditions of the photovoltaic maximum access capacity evaluation original model of the power distribution network system comprise equality constraint and inequality constraint; wherein the equality constraint is a system power flow constraint; inequality constraints are control variable upper and lower limit constraints and state variable upper and lower limit constraints.
The method of the application is further improved in that the step of obtaining the objective function of the photovoltaic maximum access capacity evaluation original model of the power distribution network system comprises the following steps:
1) Establishing an objective function of a model:
the expression of the maximum objective function of the total capacity of the distributed photovoltaic access is that,
in the formula ,PPV,i Representing the distributed photovoltaic access at the ith node; n (N) PV Representing the total number of distributed photovoltaic access nodes;
the expression of the network active power loss minimum objective function of the system operation is that,
in the formula ,Iij Transmitting current for line ij; r is (r) ij The resistance of the line ij; v (V) ij Is the voltage of node i; p (P) ij 、Q ij The transmission power of the head end of the line ij;
2) Based on the objective function of the step 1), the model is standardized, and the standardized distributed photovoltaic access capacity and the network active power loss are obtained; wherein,
the expression for the normalization is that,
wherein ω is a target to be optimized; omega max 、ω min Representing the maximum and minimum of the primitive function, respectively.
The method is further improved in that the constraint condition of the photovoltaic maximum access capacity evaluation original model of the power distribution network system comprises equality constraint and inequality constraint; wherein the equality constraint is a system power flow constraint; inequality constraints are control variable upper and lower limit constraints and state variable upper and lower limit constraints,
the system flow constraint is described by adopting a branch flow equation, the expression is that,
in the formula ,V1 Is the balanced node voltage; v (V) ref Is V (V) 1 Is a reference value of (2); v (V) j The voltage amplitude at node j; p (P) jk 、Q jk J.fwdarw.k represents the set of all lines directed from node j to node k for the transmission power of the head end of line jk; r is (r) ij 、x ij The resistance and reactance of the line ij respectively; i ij For the current flowing through the line ij;the active load and the reactive load of the node j are respectively;active power and reactive power emitted by node j distributed photovoltaic respectively;
the node voltage constraint expression is that,
1-ε≤V j ≤1+ε；
wherein ε represents the allowable voltage deviation amount;
the line current carrying capacity constraint expression is that,
in the formula ,Iij For the current flowing through the line ij;maximum current value allowed to be transmitted for line ij;
the distributed photovoltaic capacity constraint expression is that,
in the formula ,SDPV,i Representing the access capacity of the ith node distributed photovoltaic,representing the maximum capacity a node is allowed to access the distributed photovoltaic;
the flow reverse constraint expression is that,
P re ≤0；
in the formula ,Pre Representing the power transmitted from the low-voltage side to the high-voltage side of the main transformer of the power distribution network.
The method of the application is further improved in that in the step of carrying out the convexity on the original photovoltaic maximum access capacity evaluation model of the power distribution network system to obtain the convex quadratic programming model,
carrying out convexity by adopting a method for simplifying a tide equation; the simplifying assumption is that the active loss on the line is far less than the power transmitted by the line itself; the voltage deviation between the nodes is far smaller than the node voltage itself;
the photovoltaic maximum access capacity evaluation model after the convexity is that,
in the formula ,U i ＝V i 2 。
the method is further improved in that in the step of establishing the partition-based distributed photovoltaic maximum access capacity assessment model based on the power distribution network system partition and the convex quadratic programming model,
the power distribution network system is divided into R associated physical areas, which are represented by a set R; for a certain area a, N is used for a Representing the node set of region a, denoted E a Representing the set of branches of region a, e ij ∈E a A certain branch representing region a; coupling branch e ij The state variable of (2) includes the power P of the branch transmission ij 、Q ij Voltage square U of two end nodes of branch i 、U j The method comprises the steps of carrying out a first treatment on the surface of the Vector for state of coupling branch in region aA representation;
in order to make the problem of partition solving equivalent to the original problem, the state variables of the coupling branches obtained by the adjacent regional sub-problems must be equal, and the expression of the partition coordinated distributed photovoltaic maximum access capacity evaluation model converted by the model is that,
in the formula ,fa (x a ) An objective function representing a region a sub-problem; h is a a (x a ) Constraint for the corresponding equation; g a (x a ) Constraint for the corresponding inequality; x is x a Representing the set of all variables within region aRegion a is adjacent to region b.
The method of the application is further improved in that the step 2 specifically comprises the following steps:
establishing an augmented Lagrangian function corresponding to an objective function of a region a and region b sub-optimization problem based on a partition coordination-based distributed photovoltaic maximum access capacity evaluation model and />And transforming the obtained product, wherein the transformed extended Lagrangian function is,
wherein n is the iteration number; lambda (lambda) a and λb Is the dual variable of region a and region b; ρ is the penalty parameter of the ADMM algorithm; and />Taking the average value of the branch coupling states obtained by the nth iteration of the region a and the region b, and performing +.>
Determining constraint conditions of sub-optimization problems of all areas; wherein, for region a, the constraint is as follows:
and carrying out distributed solving based on the sub-optimization problem of each region.
The method is further improved in that the step of carrying out distributed solving based on each region sub-optimization problem specifically comprises the following steps:
1) N+1st iteration, each region respectively solves sub-optimization problem of the region, and parallel calculation solution leads to the augmentation of Lagrangian function and />A minimum decision variable value; acquiring the state of each area coupling branch> and /> wherein ,
2) Calculating the average value of the states of the coupling branches as a fixed reference value of the next iteration, wherein the calculation expression is as follows,
3) Each region updates the dual variables of the region as follows:
the algorithm convergence criterion is that boundary residual errors between adjacent areas tend to be zero; the boundary residual is defined as the square of the two norms of the differences between the adjacent region tributary states,delta is convergence accuracy; when the condition is satisfied, the iteration ends.
The application provides an ADMM-based distributed photovoltaic maximum access capacity evaluation system, which comprises the following components:
the model acquisition module is used for acquiring a partition-based distributed photovoltaic maximum access capacity evaluation model based on the power distribution network partition;
and the solving module is used for carrying out distributed solving on the partition-based distributed photovoltaic maximum access capacity evaluation model based on the synchronous ADMM algorithm to obtain a distributed photovoltaic optimal access strategy.
The system of the application is further improved in that, in the model acquisition module, the step of executing the partition-based distribution network to acquire the partition-based distributed photovoltaic maximum access capacity assessment model comprises the following steps:
acquiring a photovoltaic maximum access capacity evaluation original model of a power distribution network system;
carrying out convexity on a photovoltaic maximum access capacity evaluation original model of the power distribution network system to obtain a convex quadratic programming model;
establishing a partition-based distributed photovoltaic maximum access capacity assessment model based on a power distribution network system partition and a convex quadratic programming model;
wherein, the objective function of the photovoltaic maximum access capacity evaluation original model of the power distribution network system is that,
F＝α 1 F PV +α 2 F loss ；
in the formula ,α1 、α 2 Is a weight coefficient; f (F) PV 、F loss Respectively standardized distributed photovoltaic access capacity and active power loss of a network;
the constraint conditions of the photovoltaic maximum access capacity evaluation original model of the power distribution network system comprise equality constraint and inequality constraint; wherein the equality constraint is a system power flow constraint; inequality constraints are control variable upper and lower limit constraints and state variable upper and lower limit constraints.
Compared with the prior art, the application has the following beneficial effects:
according to the method for evaluating the maximum access capacity of the distributed photovoltaic based on the ADMM, the model for evaluating the maximum access capacity of the distributed photovoltaic is established, and the model is subjected to distributed solution by adopting a synchronous ADMM algorithm, so that the optimal access strategy of the distributed photovoltaic can be obtained.
Specifically, the application establishes the maximum access capacity evaluation of the distributed photovoltaic based on the partition coordination and the convex optimization, comprehensively considers the access capacity of the distributed photovoltaic and the active power loss of the system, and adopts an ADMM distributed optimization algorithm to determine the optimal access point and the access capacity of the distributed photovoltaic under different operation conditions. Compared with the existing centralized calculation, the method can improve the access capacity of the distributed photovoltaic to a certain extent, and can reduce the active power loss on the line.
In the application, the distributed photovoltaic access capacity and the active power loss of the power distribution network line are taken as objective functions, and the constraint of a power flow equation of the power distribution network, the constraint of node voltage, the constraint of the current carrying capacity of the line and the like are considered; the non-convex optimization problem is converted into a convex quadratic programming problem by using a simplified branch flow equation, the convex quadratic programming problem is solved in a distributed mode in a physical partition mode by adopting a synchronous ADMM algorithm, and finally the access strategy of the distributed photovoltaic of each region under different operation conditions can be obtained.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following description of the embodiments or the drawings used in the description of the prior art will make a brief description; it will be apparent to those of ordinary skill in the art that the drawings in the following description are of some embodiments of the application and that other drawings may be derived from them without undue effort.
Fig. 1 is a schematic flow chart of a distributed photovoltaic maximum access capacity assessment method based on ADMM according to an embodiment of the present application;
FIG. 2 is a schematic diagram of a branch tidal current equation in an embodiment of the present application;
FIG. 3 is a schematic diagram of an IEEE-33 node distribution network system in accordance with an embodiment of the present application;
FIG. 4 is a schematic diagram of an algorithm solution flow in an embodiment of the present application;
fig. 5 is a schematic diagram of access capacity of each node in an embodiment of the present application;
FIG. 6 is a schematic diagram of a voltage curve during distributed access according to an embodiment of the present application;
FIG. 7 is a schematic diagram of an algorithm optimizing curve in an embodiment of the present application;
fig. 8 is a schematic diagram of an ADMM-based distributed photovoltaic maximum access capacity assessment system according to an embodiment of the present application.
Detailed Description
In order that those skilled in the art will better understand the present application, a technical solution in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in which it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present application without making any inventive effort, shall fall within the scope of the present application.
It should be noted that the terms "first," "second," and the like in the description and the claims of the present application and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the application described herein may be implemented in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The application is described in further detail below with reference to the attached drawing figures:
referring to fig. 1, an ADMM-based method for evaluating a maximum access capacity of a distributed photovoltaic according to an embodiment of the present application specifically includes the following steps:
step 1, based on power distribution network subareas, acquiring a subarea-based distributed photovoltaic maximum access capacity evaluation model;
and 2, carrying out distributed solution on the partition-based distributed photovoltaic maximum access capacity evaluation model based on a synchronous ADMM algorithm to obtain a distributed photovoltaic optimal access strategy.
According to the method provided by the embodiment of the application, the maximum access capacity evaluation model of the distributed photovoltaic is established based on the partition coordination and convex optimization ideas, and the model is subjected to distributed solution by adopting the synchronous ADMM algorithm, so that the optimal access strategy of the distributed photovoltaic can be obtained.
In the embodiment of the application, step 1, based on power distribution network partition, the step of obtaining a partition-based distributed photovoltaic maximum access capacity evaluation model specifically comprises the following steps:
establishing a photovoltaic maximum access capacity evaluation model of the power distribution network system, and carrying out convexity on the model; then partitioning the power distribution network system, and establishing a partition-based distributed photovoltaic maximum access capacity evaluation model; wherein,
(1) The objective function of the photovoltaic maximum access capacity evaluation model of the power distribution network system comprises the following steps:
the objective function I, the maximum total capacity of the distributed photovoltaic access, the expression is,
in the formula ,PPV,i Represent the first i Distributed photovoltaic access at individual nodes; n (N) PV Representing the total number of distributed photovoltaic access nodes.
And the active power loss of the network operated by the system is minimum, and the expression is as follows:
in the formula ,Iij Transmitting current for line ij; r is (r) ij The resistance of the line ij; v (V) ij Is a node i Is a voltage of (2); p (P) ij 、Q ij Is the transmission power of the head end of the line ij.
Taking into account the weight problem of the actual system, normalizing the target, normalizing the values of various variables to be within the range of (0, 1), normalizing the model by adopting the following method,
wherein ω is a target to be optimized; omega max 、ω min Representing the maximum and minimum of the primitive function, respectively.
And carrying out weighted summation on the two standardized objective functions to obtain a new objective function, wherein the new objective function is as follows:
F＝α 1 F PV +α 2 F loss
in the formula ：α1 、α 2 Is a weight coefficient; f (F) PV 、F loss Respectively is marked withThe standardized distributed photovoltaic access capacity and the active power loss of the network.
(2) The constraint conditions of the photovoltaic maximum access capacity evaluation model of the power distribution network system comprise equality constraint and inequality constraint; the equality constraint is a system power flow constraint, and the inequality constraint is mainly a control variable upper limit constraint and a control variable lower limit constraint and a state variable upper limit and lower limit constraint.
1) System power flow constraint
The system power flow constraint is described by adopting a branch power flow equation, and for the radial network shown in fig. 2, the influence of the line on the ground capacitance and susceptance is ignored, and according to kirchhoff voltage current law, a power flow equation (DistFlow) which can be described in a branch form is as follows:
in the formula ,V1 Is the balanced node voltage; v (V) ref Is V (V) 1 Is a reference value of (2); v (V) j The voltage amplitude at node j; p (P) jk 、Q jk J.fwdarw.k represents the set of all lines directed from node j to node k for the transmission power of the head end of line jk; r is (r) ij 、x ij The resistance and reactance of the line ij respectively; i ij For the current flowing through the line ij;the active load and the reactive load of the node j are respectively;active power and reactive power emitted by the node j distributed photovoltaic are respectively.
2) Node voltage constraint
The voltage of each node is required to meet the safety constraint in the operation of the power grid and is kept near the rated voltage, as follows:
1-ε≤V j ≤1+ε
wherein: ε represents the allowable voltage deviation and is typically 0.05pu.
3) Line current carrying capacity constraints
in the formula ：Iij For the current flowing through the line ij;the maximum current value allowed to be transmitted for line ij.
4) Distributed photovoltaic capacity constraint
in the formula ：SDPV,i Representing the access capacity of the ith node distributed photovoltaic,representing the maximum capacity that a node is allowed to access the distributed photovoltaic.
5) Reverse constraint of tide
P re ≤0
in the formula ：Pre Representing the power transmitted from the low-voltage side to the high-voltage side of the main transformer of the power distribution network.
(3) In the step of carrying out the salifying on the model, a method for reasonably simplifying a DistFlow flow equation is adopted to carry out the salifying on the original optimization problem; wherein,
the simplifying assumption is: 1) The active loss on the line is much smaller than the power transmitted by the line itself; 2) The voltage deviation between the nodes is far smaller than the node voltage itself;
based on the two assumptions, the quadratic term in the DistFlow flow equation is negligible, and the voltage amplitude V in the objective function i The voltage amplitude V of the balance node can be approximated 1 ；
The photovoltaic maximum access capacity evaluation model of the system can be simplified into,
in the formula ：U i ＝V i 2 。
After the original optimization problem is simplified, the original optimization problem is converted into a convex quadratic programming model with a quadratic objective function and a linear constraint condition through variable replacement; according to the optimization theory, the local optimal solution of the convex optimization problem is equal to the global optimal solution. Therefore, a distributed optimization algorithm may be used to find the optimal solution to the problem.
(4) Partitioning a power distribution network system, wherein in the step of establishing a partition-based distributed photovoltaic maximum access capacity evaluation model, the power distribution network system is divided into R associated physical areas, and the R associated physical areas are represented by a set R; for a certain area a, N is used for a Representing the node set of region a, denoted E a Representing the set of branches of region a, e ij ∈E a A certain branch of region a is indicated.
Taking the IEEE-33 node distribution network shown in fig. 3 as an example, the network totally comprises 32 branches and 5 interconnecting switch branches, and is divided into 3 areas, and according to the partition method, the areas a: {1-7,18-15,33}, b: {6-17}, c: {5,25-32}, are respectively represented by node sets. Region a and region b pass through branch e 67 Coupled, region a and region c pass through branch e 525 And (3) coupling. Coupling branch e ij The state variable of (2) includes the power P of the branch transmission ij 、Q ij Voltage square U of two end nodes of branch i 、U j . The states of the coupling branches in region a can be used as vectorsAnd (3) representing.
In order to make the problem of partition solution equivalent to the original problem, the state variables of the coupling branches obtained by the adjacent region sub-problems must be equal. Thus, the original model can be converted into a zoned coordinated distributed photovoltaic maximum access capacity assessment model:
in the formula ：fa (x a ) An objective function representing a region a sub-problem; h is a a (x a ) Constraint for its corresponding equation; g a (x a ) Constraint for its corresponding inequality; x is x a Representing the set of all variables within region aRegion a is adjacent to region b.
In the embodiment of the application, the step of obtaining the optimal access strategy of the distributed photovoltaic specifically comprises the following steps of:
establishing an augmented Lagrangian function corresponding to an objective function of a region a and region b sub-optimization problem based on a partition coordination-based distributed photovoltaic maximum access capacity evaluation model and />And carrying out proper transformation on the obtained product, wherein the obtained product has the following augmentation Lagrangian function:
wherein n is the number of iterations, lambda a and λb P is the penalty parameter for the ADMM algorithm, which is the dual variable for region a and region b. and />Taking an average value of the coupling states of the branches obtained by the nth iteration of the region a and the region b, wherein the average value is as follows:
determining constraint conditions of sub-optimization problems of each region:
taking area a as an example, the constraint is as follows,
after the sub-optimization problem of each region is clear, each region controller can perform distributed solution on the model according to the flowchart shown in fig. 4, and specific steps are as follows:
1) N+1st iteration, each region respectively solves sub-optimization problem of the region, and parallel calculation solution leads to the augmentation of Lagrangian function and />Minimum decision variable value, and simultaneously acquiring the state of each regional coupling branch> and />
2) The average value of the states of the coupling branches is calculated as shown in the following equation as a fixed reference value for the next iteration.
3) Each region updates the dual variables of the region as follows:
/>
the criterion for algorithm convergence is that the boundary residual between adjacent regions tends to zero. The boundary residual is defined as the square of the two norms of the difference between the adjacent region tributary states as follows:
in the formula, delta is convergence accuracy, and when the above conditions are satisfied, the iteration is ended.
The embodiment of the application is specifically and exemplarily used for selecting No. 3-17 nodes on a main line as distributed photovoltaic single centralized access test nodes, and the optimal access capacity of each node under different power factors lambda is shown in a table 1.
TABLE 1 centralized access optimal Capacity (MW)
As can be seen from the data in table 1, the closer the distributed photovoltaic access point is to the end of the line, the lower its optimal access capacity, because the end of the line is more sensitive to the access of the distributed photovoltaic, and the reactive power emitted by the distributed photovoltaic makes the voltage of the node easier to overrun. When the distributed photovoltaic access point moves forward, reactive power emitted by the distributed photovoltaic access point gradually acts on the whole network, so that the sensitivity degree of the node to voltage is reduced, the node is not easy to overrun, and at the moment, the flow reversal and the line current-carrying constraint become main factors for restricting the capacity of the distributed photovoltaic access.
At the end of the line, the access capacity of the distributed photovoltaic is gradually reduced along with the reduction of the power factor, because the voltage is greatly influenced by reactive power, and the reactive power emitted by the distributed photovoltaic is increased along with the reduction of the power factor, so that the voltage of the access point is easier to be out of limit. As the access point moves forward, the reactive power sensitivity to voltage decreases, and the lower the power factor, the greater the distributed photovoltaic access capacity.
All nodes are tested as access points of distributed photovoltaics, the access capacity of each node is shown in figure 5 when the power factor is 1, the total capacity of the distributed photovoltaics accessed by the system is 4.88MW, and the total active power loss of the system is 76.87kW.
Table 2 shows the access capacity and active power loss of the distributed photovoltaic at different power factors, and fig. 6 shows the node voltages when the access capacity of each node distributed photovoltaic at different power factors is optimal.
TABLE 2 distributed access to optimal capacity and active loss
As can be seen from fig. 6 and table 2, the smaller the power factor of the system is, the larger the distributed photovoltaic capacity the system can accept, the lower the active power loss on the line is, and the voltage level of each node is obviously improved.
When the power factor lambda is 0.9, the convergence curve of the ADMM algorithm is as shown in FIG. 7, and as can be seen from FIG. 7, the algorithm is close to convergence when iterated about 60 times, and the final boundary residual is 7.64×10 -16 The convergence speed of the algorithm is high, and the solving error is small.
In summary, the embodiment of the application discloses an ADMM-based method for evaluating the maximum access capacity of a distributed photovoltaic, which considers the technical defects of high centralized calculation cost, high communication requirement and poor reliability, and is difficult to adapt to the actual requirements of a power distribution network accessed in a large scale by the distributed photovoltaic; the application discloses an ADMM-based distributed photovoltaic maximum access capacity assessment method based on the ideas of partition coordination control and convex optimization, which takes distributed photovoltaic access capacity and active power loss of a power distribution network line as objective functions, and considers power distribution network tide equation constraint, node voltage constraint, line current carrying capacity constraint and the like. The non-convex optimization problem is converted into a convex quadratic programming problem by using a simplified branch flow equation, the convex quadratic programming problem is solved in a distributed mode in a physical partition mode by adopting a synchronous ADMM algorithm, and the access strategy of the distributed photovoltaic of each region under different operation conditions is obtained.
The following are device embodiments of the present application that may be used to perform method embodiments of the present application. For details not disclosed in the apparatus embodiments, please refer to the method embodiments of the present application.
Referring to fig. 8, in still another embodiment of the present application, an ADMM-based system for evaluating maximum access capacity of a distributed photovoltaic is provided, comprising:
the model acquisition module is used for acquiring a partition-based distributed photovoltaic maximum access capacity evaluation model based on the power distribution network partition;
and the solving module is used for carrying out distributed solving on the partition-based distributed photovoltaic maximum access capacity evaluation model based on the synchronous ADMM algorithm to obtain a distributed photovoltaic optimal access strategy.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical aspects of the present application and not for limiting the same, and although the present application has been described in detail with reference to the above embodiments, it should be understood by those of ordinary skill in the art that: modifications and equivalents may be made to the specific embodiments of the application without departing from the spirit and scope of the application, which is intended to be covered by the claims.
Claims (10)
1. An ADMM-based distributed photovoltaic maximum access capacity assessment method is characterized by comprising the following steps:
step 1, based on power distribution network subareas, acquiring a subarea-based distributed photovoltaic maximum access capacity evaluation model;
and 2, carrying out distributed solution on the partition-based distributed photovoltaic maximum access capacity evaluation model based on a synchronous ADMM algorithm to obtain a distributed photovoltaic optimal access strategy.
2. The method for evaluating the maximum access capacity of a distributed photovoltaic system based on ADMM according to claim 1, wherein step 1 specifically comprises:
acquiring a photovoltaic maximum access capacity evaluation original model of a power distribution network system;
carrying out convexity on a photovoltaic maximum access capacity evaluation original model of the power distribution network system to obtain a convex quadratic programming model;
establishing a partition-based distributed photovoltaic maximum access capacity assessment model based on a power distribution network system partition and a convex quadratic programming model;
wherein, the objective function of the photovoltaic maximum access capacity evaluation original model of the power distribution network system is that,
F＝α 1 F PV +α 2 F loss ；
in the formula ,α1 、α 2 Is a weight coefficient; f (F) PV 、F loss Respectively standardized distributed photovoltaic access capacity and active power loss of a network;
the constraint conditions of the photovoltaic maximum access capacity evaluation original model of the power distribution network system comprise equality constraint and inequality constraint; wherein the equality constraint is a system power flow constraint; inequality constraints are control variable upper and lower limit constraints and state variable upper and lower limit constraints.
3. The method for evaluating the photovoltaic maximum access capacity of the power distribution network system based on the ADMM according to claim 2, wherein the step of obtaining the objective function of the photovoltaic maximum access capacity evaluation model of the power distribution network system comprises the following steps:
1) Establishing an objective function of a model:
the expression of the maximum objective function of the total capacity of the distributed photovoltaic access is that,
in the formula ,PPV,i Representing the distributed photovoltaic access at the ith node; n (N) PV Representing the total number of distributed photovoltaic access nodes;
the expression of the network active power loss minimum objective function of the system operation is that,
in the formula ,Iij Transmitting current for line ij; r is (r) ij The resistance of the line ij; v (V) ij Is the voltage of node i; p (P) ij 、Q ij The transmission power of the head end of the line ij;
2) Based on the objective function of the step 1), the model is standardized, and the standardized distributed photovoltaic access capacity and the network active power loss are obtained; wherein,
the expression for the normalization is that,
wherein ω is a target to be optimized; omega max 、ω min Representing the maximum and minimum of the primitive function, respectively.
4. The method for evaluating the photovoltaic maximum access capacity based on the ADMM as claimed in claim 2, wherein the constraint condition of the photovoltaic maximum access capacity evaluating original model of the power distribution network system comprises equality constraint and inequality constraint; wherein the equality constraint is a system power flow constraint; inequality constraints are control variable upper and lower limit constraints and state variable upper and lower limit constraints,
the system flow constraint is described by adopting a branch flow equation, the expression is that,
in the formula ,V1 Is the balanced node voltage; v (V) ref Is V (V) 1 Is a reference value of (2); v (V) j The voltage amplitude at node j; p (P) jk 、Q jk J.fwdarw.k represents the set of all lines directed from node j to node k for the transmission power of the head end of line jk; r is (r) ij 、x ij The resistance and reactance of the line ij respectively; i ij For the current flowing through the line ij;the active load and the reactive load of the node j are respectively;active power and reactive power emitted by node j distributed photovoltaic respectively;
the node voltage constraint expression is that,
1-ε≤V j ≤1+ε；
wherein ε represents the allowable voltage deviation amount;
the line current carrying capacity constraint expression is that,
in the formula ,Iij For the current flowing through the line ij;maximum current value allowed to be transmitted for line ij;
the distributed photovoltaic capacity constraint expression is that,
in the formula ,SDPV,i Representing the access capacity of the ith node distributed photovoltaic,representing the maximum capacity a node is allowed to access the distributed photovoltaic;
the flow reverse constraint expression is that,
P re ≤0；
in the formula ,Pre Representing the power transmitted from the low-voltage side to the high-voltage side of the main transformer of the power distribution network.
5. The method for evaluating photovoltaic maximum access capacity based on ADMM as claimed in claim 4, wherein in said step of obtaining a convex quadratic programming model by performing the convex on the photovoltaic maximum access capacity evaluating original model of the power distribution network system,
carrying out convexity by adopting a method for simplifying a tide equation; the simplifying assumption is that the active loss on the line is far less than the power transmitted by the line itself; the voltage deviation between the nodes is far smaller than the node voltage itself;
the photovoltaic maximum access capacity evaluation model after the convexity is that,
in the formula ,U i ＝V i 2 。
6. the method for estimating maximum access capacity of a distributed photovoltaic system based on ADMM as claimed in claim 5, wherein in said step of establishing the estimation model of maximum access capacity of a distributed photovoltaic system based on the power distribution network system partition and convex quadratic programming model,
the power distribution network system is divided into R associated physical areas, which are represented by a set R; for a certain area a, N is used for a Representing the node set of region a, denoted E a Representing the set of branches of region a, e ij ∈E a A certain branch representing region a; coupling branch e ij The state variable of (2) includes the power P of the branch transmission ij 、Q ij Voltage square U of two end nodes of branch i 、U j The method comprises the steps of carrying out a first treatment on the surface of the Vector for state of coupling branch in region aA representation;
in order to make the problem of partition solving equivalent to the original problem, the state variables of the coupling branches obtained by the adjacent regional sub-problems must be equal, and the expression of the partition coordinated distributed photovoltaic maximum access capacity evaluation model converted by the model is that,
in the formula ,fa (x a ) An objective function representing a region a sub-problem; h is a a (x a ) Constraint for the corresponding equation; g a (x a ) Constraint for the corresponding inequality; x is x a Representing the set of all variables within region aRegion a is adjacent to region b.
7. The method for evaluating the maximum access capacity of a distributed photovoltaic system based on ADMM according to claim 6, wherein step 2 comprises:
establishing an augmented Lagrangian function corresponding to an objective function of a region a and region b sub-optimization problem based on a partition coordination-based distributed photovoltaic maximum access capacity evaluation model and />And transform it intoThe converted augmented lagrangian function is,
wherein n is the iteration number; lambda (lambda) a and λb Is the dual variable of region a and region b; ρ is the penalty parameter of the ADMM algorithm;andtaking the average value of the branch coupling states obtained by the nth iteration of the region a and the region b, and performing +.>
Determining constraint conditions of sub-optimization problems of all areas; wherein, for region a, the constraint is as follows:
and carrying out distributed solving based on the sub-optimization problem of each region.
8. The method for evaluating the maximum access capacity of a distributed photovoltaic system based on the ADMM according to claim 7, wherein the step of performing the distributed solution based on the sub-optimization problem of each region specifically comprises:
1) N+1st iteration, each region respectively solves sub-optimization problem of the region, and parallel calculation solution leads to the augmentation of Lagrangian function and />A minimum decision variable value; acquiring the state of each area coupling branch and /> wherein ,
2) Calculating the average value of the states of the coupling branches as a fixed reference value of the next iteration, wherein the calculation expression is as follows,
3) Each region updates the dual variables of the region as follows:
the algorithm convergence criterion is that boundary residual errors between adjacent areas tend to be zero; the boundary residual is defined as the square of the two norms of the differences between the adjacent region tributary states,delta is convergence accuracy; when the conditions areAnd when the result is satisfied, ending the iteration.
9. An ADMM-based distributed photovoltaic maximum access capacity assessment system, comprising:
the model acquisition module is used for acquiring a partition-based distributed photovoltaic maximum access capacity evaluation model based on the power distribution network partition;
and the solving module is used for carrying out distributed solving on the partition-based distributed photovoltaic maximum access capacity evaluation model based on the synchronous ADMM algorithm to obtain a distributed photovoltaic optimal access strategy.
10. The ADMM-based distributed photovoltaic maximum access capacity assessment system of claim 9, wherein the step of performing the partition-based distribution network in the model acquisition module to acquire the partition-based distributed photovoltaic maximum access capacity assessment model comprises:
acquiring a photovoltaic maximum access capacity evaluation original model of a power distribution network system;
carrying out convexity on a photovoltaic maximum access capacity evaluation original model of the power distribution network system to obtain a convex quadratic programming model;
establishing a partition-based distributed photovoltaic maximum access capacity assessment model based on a power distribution network system partition and a convex quadratic programming model;
wherein, the objective function of the photovoltaic maximum access capacity evaluation original model of the power distribution network system is that,
F＝α 1 F PV +α 2 F loss ；
in the formula ,α1 、α 2 Is a weight coefficient; f (F) PV 、F loss Respectively standardized distributed photovoltaic access capacity and active power loss of a network;
the constraint conditions of the photovoltaic maximum access capacity evaluation original model of the power distribution network system comprise equality constraint and inequality constraint; wherein the equality constraint is a system power flow constraint; inequality constraints are control variable upper and lower limit constraints and state variable upper and lower limit constraints.
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