CN113098017A - Calculation method and calculation device for alternating current power flow unit combination - Google Patents
Calculation method and calculation device for alternating current power flow unit combination Download PDFInfo
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- CN113098017A CN113098017A CN202110391216.5A CN202110391216A CN113098017A CN 113098017 A CN113098017 A CN 113098017A CN 202110391216 A CN202110391216 A CN 202110391216A CN 113098017 A CN113098017 A CN 113098017A
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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
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
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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
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
Abstract
The application provides a calculation method and a calculation device for an alternating current power flow unit combination. The calculation method comprises the following steps: establishing a main problem of an alternating current power flow unit combination based on piecewise linear relaxation; establishing a subproblem of an alternating current power flow unit combination based on a fixed integer variable; and solving the main problem and the sub-problems by adopting an alternating iteration algorithm to obtain the optimal solution of the alternating current power flow unit combination, and obtaining the more accurate optimal solution of the alternating current power flow unit combination by adopting the scheme.
Description
Technical Field
The application relates to the field of power systems, in particular to a computing method, a computing device, a computer-readable storage medium and a processor of an alternating current power flow unit combination.
Background
The power system unit combination is based on the premise of safe and reliable power supply for users, and a start-stop plan of the unit in the future day is made in advance, so that the running cost or fuel cost of the power system is the lowest. Compared with the traditional unit combination, the alternating current power flow unit combination considers the equivalent constraint of the alternating current power flow, so that the reactive power balance and the voltage safety of the system are further ensured. However, the problem of the alternating current power flow unit combination is difficult to calculate reliably and efficiently due to the non-convexity of the alternating current power flow equality constraint and the integral variable, the alternating current power flow equality constraint is converted into the constraint which is easy to process by the traditional linearization or relaxation method, and although the alternating current power flow unit combination can be effectively calculated, the problem of limited precision or overlarge relaxation gap exists, so that the solution result is unreliable, and even the requirement of safe operation of the power system cannot be met.
Disclosure of Invention
The main purpose of the present application is to provide a calculation method, a calculation apparatus, a computer-readable storage medium, and a processor for an alternating current power flow unit combination, so as to solve the problem that the accuracy of the calculation method for the alternating current power flow unit combination in the prior art is limited.
In order to achieve the above object, according to an aspect of the present application, there is provided a method for calculating an ac power flow unit combination, including: establishing a main problem of an alternating current power flow unit combination based on piecewise linear relaxation; establishing a subproblem of the alternating current power flow unit combination based on a fixed integer variable; and solving the main problem and the sub-problems by adopting an alternating iteration algorithm to obtain an optimal solution of the alternating current power flow unit combination.
Further, solving the main problem and the sub-problems by adopting an alternating iteration algorithm to obtain an optimal solution of the alternating current power flow unit combination, wherein the optimal solution comprises the following steps: solving the main problem by adopting a branch-and-bound algorithm to obtain an optimal solution of the main problem; solving the sub-problem based on an interior point method; if the sub-problem is feasible, obtaining an optimal solution of the alternating current power flow unit combination; if the sub-problem is not feasible, establishing a relaxation sub-problem of the alternating current power flow unit combination based on the fixed integer variable; constructing Benders cut constraints according to the relaxor problems; and adding Benders cut constraint to the main problem to iteratively solve again.
Further, the main problem comprises a first objective function and a first constraint condition, wherein the first constraint condition comprises a generator starting constraint, a generator minimum on-off time constraint, a generator output constraint, a generator rotation standby constraint, a generator climbing constraint, a node power balance constraint, an alternating current power flow equation constraint based on piecewise linear relaxation and a node voltage safety constraint.
Further, the sub-problems comprise a second objective function and second constraint conditions, wherein the second constraint conditions comprise generator output constraint, generator rotation standby constraint, generator climbing constraint, node power balance constraint, node voltage safety constraint, strict alternating current power flow equation constraint and constraint that the starting and stopping state variables of the fixed generator set are the optimal solution of the current main problem.
Further, the relaxation subproblem comprises a third objective function and a third constraint condition, wherein the third constraint condition comprises generator output constraint, generator rotation standby constraint, generator climbing constraint, node voltage safety constraint, strict alternating current power flow equation constraint, node power balance constraint for introducing relaxation power and constraint for fixing the starting and stopping state variable of the generator set as the optimal solution of the current main problem.
Further, constructing Benders cut constraints from the relaxor problem, including: obtaining an optimal objective function value of the relaxation sub-problem; obtaining a Lagrange multiplier corresponding to the constraint that the starting and stopping state variable of the fixed generator set is the optimal solution of the current main problem; and constructing the Benders cut constraint according to the optimal objective function value and the Lagrangian multiplier.
Further, the optimal solution of the alternating current power flow unit combination comprises a start-stop plan, a supply amount of a rotation reserve, a planned value of active power and a planned value of reactive power of all the generators in the next day.
According to another aspect of the application, a computing device of an alternating current power flow unit combination is provided, which includes: the first establishing unit is used for establishing a main problem of the alternating current power flow unit combination based on piecewise linear relaxation; the second establishing unit is used for establishing a subproblem of the alternating current power flow unit combination based on a fixed integer variable; and the solving unit is used for solving the main problem and the sub-problems by adopting an alternating iteration algorithm to obtain the optimal solution of the alternating current power flow unit combination.
According to another aspect of the application, a computer-readable storage medium is provided, and the computer-readable storage medium includes a stored program, where the program, when executed, controls a device in which the computer-readable storage medium is located to perform any one of the methods for calculating the ac power flow unit combination.
According to another aspect of the application, a processor is provided, and the processor is configured to execute a program, where the program executes a method for calculating any one of the ac power flow unit combinations.
By applying the technical scheme, aiming at the combination problem of the alternating current power flow unit of the power system, the original problem is decomposed into a main problem of piecewise linear relaxation and a sub-problem of fixed integer variables, and then the solution is carried out through an alternating iteration algorithm. Since the main problem employs piecewise linear relaxation, the mixed integer nonlinear programming problem is transformed into a mixed integer linear programming problem, which can be computed more efficiently. And obtaining a more accurate optimal solution of the alternating current power flow unit combination.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application. In the drawings:
fig. 1 shows a flow chart of a calculation method of an alternating current power flow unit combination according to an embodiment of the application;
fig. 2 shows a schematic diagram of a computing device of an ac power flow unit combination according to an embodiment of the present application.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
In order to make the technical solutions better understood by those skilled in the art, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only partial embodiments of the present application, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
It should be noted that the terms "first," "second," and the like in the description and claims of this application and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It should be understood that the data so used may be interchanged under appropriate circumstances such that embodiments of the application described herein may be used. 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.
It will be understood that when an element such as a layer, film, region, or substrate is referred to as being "on" another element, it can be directly on the other element or intervening elements may also be present. Also, in the specification and claims, when an element is described as being "connected" to another element, the element may be "directly connected" to the other element or "connected" to the other element through a third element.
As introduced in the background art, the alternating current power flow unit combination calculation method in the prior art has a limited precision, and to solve the problem that the alternating current power flow unit combination calculation method has a limited precision, embodiments of the present application provide a calculation method, a calculation apparatus, a computer-readable storage medium, and a processor for an alternating current power flow unit combination.
According to the embodiment of the application, a calculation method of an alternating current power flow unit combination is provided.
Fig. 1 is a flowchart of a calculation method of an ac power flow unit combination according to an embodiment of the present application. As shown in fig. 1, the method comprises the steps of:
step S101, establishing a main problem of an alternating current power flow unit combination based on piecewise linear relaxation;
step S102, establishing a subproblem of the alternating current power flow unit combination based on a fixed integer variable;
and step S103, solving the main problem and the sub-problems by adopting an alternating iteration algorithm to obtain an optimal solution of the alternating current power flow unit combination.
In particular, fixed integer variables means that the integer variables in the sub-problem are fixed.
In the scheme, aiming at the alternating current power flow unit combination problem of the power system, the original problem is decomposed into a main problem of piecewise linearity relaxation and a sub-problem of fixed integer variables, and then the main problem and the sub-problem are solved through an alternating iteration algorithm. Since the main problem employs piecewise linear relaxation, the mixed integer nonlinear programming problem is transformed into a mixed integer linear programming problem, which can be computed more efficiently. And obtaining a more accurate optimal solution of the alternating current power flow unit combination.
It should be noted that the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer-executable instructions and that, although a logical order is illustrated in the flowcharts, in some cases, the steps illustrated or described may be performed in an order different than presented herein.
In an embodiment of the present application, solving the main problem and the sub-problems by using an alternating iteration algorithm to obtain an optimal solution of the alternating current power flow unit combination includes: solving the main problem by adopting a branch-and-bound algorithm to obtain an optimal solution of the main problem; solving the sub-problem based on an interior point method; if the sub-problems are feasible, obtaining an optimal solution of the alternating current power flow unit combination; if the sub-problem is not feasible, establishing a relaxation sub-problem of the alternating current power flow unit combination based on the fixed integer variable; constructing Benders cut constraints according to the relaxor problem; and adding the Benders cut constraint to the main problem to iteratively solve again. The original problem is decomposed into a main problem of piecewise linearity relaxation and a sub-problem of fixed integer variables, and then the solution is carried out through an alternating iteration algorithm. Since the main problem employs piecewise linear relaxation, the mixed integer nonlinear programming problem is transformed into a mixed integer linear programming problem, which can be computed more efficiently. And obtaining a more accurate alternating current power flow unit combination. On the other hand, if an overlarge slack clearance exists, the best solution of the Benders cut correction main problem is returned from the slack sub problem, and the problem of overlarge slack clearance is solved.
Specifically, the sub-problem is feasible, that is, a feasible solution exists in the sub-problem after the integer variables in the sub-problem are fixed, and under the condition that the sub-problem is feasible, the optimal solution of the sub-problem is solved according to an interior point method, so that the optimal solution of the alternating current power flow unit combination is obtained.
Specifically, the optimal solution of the sub-problem and the optimal solution of the main problem form the optimal solution of the alternating current power flow unit combination.
In one embodiment of the present application, the main problem includes a first objective function and a first constraint condition, and the first constraint condition includes a generator start-up constraint, a generator minimum on-off time constraint, a generator output constraint, a generator rotation standby constraint, a generator ramp-up constraint, a node power balance constraint, an ac power flow equation constraint based on piecewise linear relaxation, and a node voltage safety constraint.
In an embodiment of the present application, the sub-problem includes a second objective function and a second constraint condition, where the second constraint condition includes a generator output constraint, a generator rotation standby constraint, a generator climbing constraint, a node power balance constraint, a node voltage safety constraint, a strict ac power flow equation constraint, and a constraint that fixes a generator set start-stop state variable as an optimal solution to the current main problem. Because strict alternating current power flow constraint is adopted in the subproblems, the reliability of a calculation result is ensured. The calculation result can be used for making a starting and stopping plan of the generator in the future day, and the power system is ensured to operate at the minimum cost on the basis of ensuring safety.
In an embodiment of the present application, the relaxation subproblem includes a third objective function and a third constraint condition, where the third constraint condition includes a generator output constraint, a generator rotation standby constraint, a generator climbing constraint, a node voltage safety constraint, a strict ac power flow equation constraint, a node power balance constraint introducing relaxation power, and a constraint fixing a generator set start-stop state variable as an optimal solution of the current main problem.
In one embodiment of the present application, constructing the Benders cut constraint based on the above-described relaxor problem includes: obtaining an optimal objective function value of the relaxor problem; obtaining a Lagrange multiplier corresponding to the constraint that the starting and stopping state variable of the fixed generator set is the optimal solution of the current main problem; and constructing the Benders cut constraint according to the optimal objective function value and the lagrange multiplier.
In an embodiment of the present application, the optimal solution of the ac power flow unit combination includes a start-stop plan, a supply amount of a rotation reserve, a planned value of active power, and a planned value of reactive power of all generators in a future day.
The embodiment of the present application further provides a computing device for an ac power flow unit combination, and it should be noted that the computing device for an ac power flow unit combination according to the embodiment of the present application may be used to execute the computing method for an ac power flow unit combination provided in the embodiment of the present application. The following describes a computing device of an ac power flow unit combination provided in an embodiment of the present application.
Fig. 2 is a schematic diagram of a computing device of an ac power flow unit combination according to an embodiment of the present application. As shown in fig. 2, the apparatus includes:
the first establishing unit 10 is used for establishing a main problem of the alternating current power flow unit combination based on piecewise linear relaxation;
a second establishing unit 20, configured to establish a subproblem of the alternating current power flow unit combination based on a fixed integer variable;
and the solving unit 30 is configured to solve the main problem and the sub-problems by using an alternating iteration algorithm to obtain an optimal solution of the alternating current power flow unit combination.
In the scheme, aiming at the alternating current power flow unit combination problem of the power system, the original problem is decomposed into a main problem of piecewise linearity relaxation and a sub-problem of fixed integer variables, and then the main problem and the sub-problem are solved through an alternating iteration algorithm. Since the main problem employs piecewise linear relaxation, the mixed integer nonlinear programming problem is transformed into a mixed integer linear programming problem, which can be computed more efficiently. And obtaining a more accurate optimal solution of the alternating current power flow unit combination.
In an embodiment of the application, the solving unit includes a first solving module, a second solving module, a determining module, an establishing module, a first constructing module and a third solving module, wherein the first solving module is configured to solve the main problem by using a branch-and-bound algorithm to obtain an optimal solution of the main problem; the second solving module is used for solving the subproblems based on an interior point method; the determining module is used for obtaining the optimal solution of the alternating current power flow unit combination if the sub-problems are feasible; the establishing module is used for establishing a relaxation subproblem of the alternating current power flow unit combination based on the fixed integer variable if the subproblem is infeasible; the first construction module is used for constructing Benders cutting constraints according to the relaxor problems; and the third solving module is used for adding Benders cut constraint to the main problem and iteratively solving again. The original problem is decomposed into a main problem of piecewise linearity relaxation and a sub-problem of fixed integer variables, and then the solution is carried out through an alternating iteration algorithm. Since the main problem employs piecewise linear relaxation, the mixed integer nonlinear programming problem is transformed into a mixed integer linear programming problem, which can be computed more efficiently. And obtaining a more accurate alternating current power flow unit combination. On the other hand, if an overlarge slack clearance exists, the best solution of the Benders cut correction main problem is returned from the slack sub problem, and the problem of overlarge slack clearance is solved.
In an embodiment of the present application, the constructing unit includes a first obtaining module, a second obtaining module, and a second constructing module, where the first obtaining module is configured to obtain an optimal objective function value of the slack sub-problem; the second acquisition module is used for acquiring a Lagrange multiplier corresponding to the constraint that the starting and stopping state variable of the fixed generator set is the optimal solution of the current main problem; and the second construction module is used for constructing the Benders cut constraint according to the optimal objective function value and the Lagrange multiplier.
The calculating device of the alternating current power flow unit combination comprises a processor and a memory, wherein the first establishing unit, the first solving unit, the second establishing unit, the second solving unit, the determining unit, the third establishing unit, the constructing unit, the third solving unit and the like are stored in the memory as program units, and the processor executes the program units stored in the memory to realize corresponding functions.
The processor comprises a kernel, and the kernel calls the corresponding program unit from the memory. One or more than one kernel can be set, and the alternating current power flow unit combination is accurately determined by adjusting kernel parameters.
The memory may include volatile memory in a computer readable medium, Random Access Memory (RAM) and/or nonvolatile memory such as Read Only Memory (ROM) or flash memory (flash RAM), and the memory includes at least one memory chip.
The embodiment of the invention provides a computer-readable storage medium, which comprises a stored program, wherein when the program runs, a device where the computer-readable storage medium is located is controlled to execute a calculation method of an alternating current power flow unit combination.
The embodiment of the invention provides a processor, which is used for running a program, wherein the program is used for executing a calculation method of an alternating current power flow unit combination during running.
The embodiment of the invention provides equipment, which comprises a processor, a memory and a program which is stored on the memory and can run on the processor, wherein when the processor executes the program, at least the following steps are realized:
step S101, establishing a main problem of an alternating current power flow unit combination based on piecewise linear relaxation;
step S102, establishing a subproblem of the alternating current power flow unit combination based on a fixed integer variable;
and step S103, solving the main problem and the sub-problems by adopting an alternating iteration algorithm to obtain an optimal solution of the alternating current power flow unit combination.
The device herein may be a server, a PC, a PAD, a mobile phone, etc.
The present application further provides a computer program product adapted to perform a program of initializing at least the following method steps when executed on a data processing device:
step S101, establishing a main problem of an alternating current power flow unit combination based on piecewise linear relaxation;
step S102, establishing a subproblem of the alternating current power flow unit combination based on a fixed integer variable;
and step S103, solving the main problem and the sub-problems by adopting an alternating iteration algorithm to obtain an optimal solution of the alternating current power flow unit combination.
As will be appreciated by one skilled in the art, 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 flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams 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.
In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include forms of volatile memory in a computer readable medium, Random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). The memory is an example of a computer-readable medium.
Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in the process, method, article, or apparatus that comprises the element.
Examples
The embodiment relates to a specific calculation method for an alternating current power flow unit combination of an electric power system. The method specifically comprises the following steps:
1) establishing an alternating current power flow unit combination main problem based on piecewise linearity relaxation; the main problem consists of an objective function and constraint conditions; the method comprises the following specific steps:
1-1) an objective function of the main question; the expression is as follows:
wherein, cgRepresenting the marginal generation cost of the g-th generator; pg,tThe active output of the g generator at the t moment is represented;
represents the start-up cost of the g-th generator; z is a radical ofg,tIndicating the starting state of the g-th generator at the t-th moment, if zg,tEqual to 1, representsThe g-th generator is started at the t-th moment if zg,tEqual to 0, indicating that the g-th generator is not started at the t-th moment;
1-2) constraints of the main problem, including:
1-2-1) generator start-up constraints:
0≤zg,t (1-2)
yg,t-yg,t-1≤zg,t (1-3)
wherein, yg,tIndicating the operating state of the g-th generator at the t-th moment if yg,tEqual to 1, means that the g-th generator is operating at the t-th moment, if yg,tEqual to 0, indicating that the g-th generator was shut down at the t-th moment;
1-2-2) minimum on-off time constraint of generator:
wherein, yg,hRepresenting the running state of the g generator at the h moment;
representing a minimum startup time interval for the g-th generator;
representing a minimum shutdown interval for the g-th generator;
1-2-3) generator output constraint:
wherein Q isg,tRepresenting the reactive power output of the g generator at the t moment; pgRepresenting the active output lower limit of the g-th generator;
representing the upper active output limit of the g-th generator; qgRepresenting the lower reactive power output limit of the g-th generator;
representing the upper reactive power output limit of the g-th generator;
indicating that the g generator rotates for standby under the active power provided at the t moment;
indicating that the g generator provides active spinning reserve at the t moment;
1-2-4) generator rotation standby constraint:
wherein the content of the first and second substances,
representing the total amount of top spin reserve required by the power system at time t;
representing the total amount of reserve for rotation of the power system at the time of the t; RU (RU)gRepresenting the uphill rate of the g-th generator; RDgRepresents the downward ramp rate of the g-th generator;
1-2-5) generator climbing restraint:
1-2-6) node power balance constraints:
wherein, Pij,t,Qij,tRespectively representing the active power and the reactive power transmitted by the ith node and the jth node at the tth moment;
respectively representing the active load power and the reactive load power of the ith node at the tth moment; j e is the i and represents that a connection line exists between the jth node and the ith node; g epsilon i represents that the g generator is positioned at the i node;
1-2-7) alternating current power flow equation constraints based on piecewise linear relaxation:
0≤wij,k,t≤1 (1-17)
wherein, gij,bij,
Respectively representing the total series conductance, the series susceptance and the parallel susceptance of the lines connected with the ith node and the jth node; thetaij,tRepresenting the phase angle difference of the line connected with the ith node and the jth node at the tth moment;
the cosine function value of the phase angle difference of the ith node and the jth node at the tth moment under the segmented relaxation is represented; vi,tRepresenting the voltage amplitude of the ith node at the t-th moment; vj,tRepresenting the voltage amplitude of the jth node at the tth moment;
representing the kth segmentation point for segmentation relaxation;
a cosine function value corresponding to a k-th segmentation point for segmentation relaxation is represented; w is aij,k,tRepresenting the weight coefficient of the kth segmentation point under the condition that the phase angle difference of the line connected with the ith node and the jth node at the t moment is subjected to segmentation relaxation;
1-2-8) node voltage safety constraints:
wherein, ViRepresents the lower voltage limit of the ith node;
represents the upper voltage limit of the ith node;
2) recording the iteration number as l, and making l equal to 0; solving the main problem of step 1) based on branch and bound algorithmTo obtain the optimal solution of the main problem
Representing the operation state result of the g generator at the t moment under the l iteration;
3) establishing an alternating current power flow unit combination sub-problem based on a fixed integer variable; the sub-problem consists of an objective function and constraint conditions;
3-1) an objective function of the sub-problem; the expression is as follows:
3-2) constraints for the sub-problem, including: (1-6) - (1-13), (1-18) and:
3-2-1) strict alternating current power flow equation constraints:
3-2-2) fixing the start-stop state variable of the generator set as the constraint of the optimal solution of the current main problem:
4) solving the sub-problem of the sub-step 3) based on an interior point method, and entering a step 7) if the sub-problem is feasible; otherwise, the subproblem is not feasible, and the step 5) is carried out;
5) establishing an alternating current power flow unit combination relaxation sub-problem based on fixed integer variables; the relaxation subproblem consists of an objective function and constraint conditions;
5-1) an objective function of the relaxation sub-problem; the expression is as follows:
wherein the content of the first and second substances,
respectively representing the slack active power and reactive power injection quantity introduced by the ith node at the tth moment;
5-2) constraints for the relaxin problem, including: (1-6) - (1-11), (1-18), (3-2), (3-3) and:
5-2-1) introduce a node power balance constraint of relaxed power:
5-2-2) fixing the start-stop state variable of the generator set as the constraint of the optimal solution of the current main problem:
6) solving the relaxation subproblem of the substep 5) based on an interior point method to obtain the optimal objective function value S of the relaxation subproblemlAnd constraining (5-4) the corresponding Lagrangian multiplier
Constructing a Benders cut constraint:
adding Benders cut constraint into constraint conditions of the main problem, enabling the iteration number l to be l +1, solving the main problem after the update constraint based on a branch-and-bound algorithm, and obtaining the optimal solution of the main problem
Entering step 3);
7) and obtaining the optimal solution of the alternating current power flow unit combination, including the start-stop plan of all the generators in the future day, the supply quantity of the rotation reserve and the plan values of active power and reactive power.
It should be noted that the present embodiment is only exemplary, and those skilled in the art can adaptively modify the formula involved in the present embodiment according to actual needs.
Aiming at the combination problem of the alternating current power flow unit of the power system, the original problem is decomposed into a main problem of piecewise linearity relaxation and a sub-problem of fixed integer variable, and then the solution is carried out through an alternating iteration algorithm. The main problem adopts piecewise linear relaxation, the mixed integer nonlinear programming problem is converted into the mixed integer linear programming problem, calculation can be carried out more efficiently, on the other hand, if an overlarge relaxation gap occurs, the relaxation subproblems are returned to Benders to cut and correct the optimal solution of the main problem, and finally, because strict alternating current power flow constraint is adopted in the subproblems, the reliability of the calculation result is ensured, the calculation result can be used for making a start-stop plan of the generator in the future day, and the power system is ensured to operate at the minimum cost on the basis of ensuring safety.
From the above description, it can be seen that the above-described embodiments of the present application achieve the following technical effects:
1) the method for calculating the alternating current power flow unit combination resolves an original problem into a main problem of piecewise linear relaxation and a sub problem of fixed integer variables aiming at the alternating current power flow unit combination problem of the power system, and then solves the main problem and the sub problem through an alternating iteration algorithm. Since the main problem employs piecewise linear relaxation, the mixed integer nonlinear programming problem is transformed into a mixed integer linear programming problem, which can be computed more efficiently. And obtaining a more accurate optimal solution of the alternating current power flow unit combination.
2) The alternating current power flow unit combination calculating device resolves an original problem into a main problem of piecewise linearity relaxation and a sub problem of fixed integer variables aiming at the alternating current power flow unit combination problem of the power system, and then solves the main problem and the sub problem through an alternating iteration algorithm. Since the main problem employs piecewise linear relaxation, the mixed integer nonlinear programming problem is transformed into a mixed integer linear programming problem, which can be computed more efficiently. And obtaining a more accurate optimal solution of the alternating current power flow unit combination.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (10)
1. A method for calculating an alternating current power flow unit combination is characterized by comprising the following steps:
establishing a main problem of an alternating current power flow unit combination based on piecewise linear relaxation;
establishing a subproblem of the alternating current power flow unit combination based on a fixed integer variable;
and solving the main problem and the sub-problems by adopting an alternating iteration algorithm to obtain an optimal solution of the alternating current power flow unit combination.
2. The method of claim 1, wherein solving the main problem and the sub-problems using an alternating iteration algorithm to obtain an optimal solution of the ac power flow unit combination comprises:
solving the main problem by adopting a branch-and-bound algorithm to obtain an optimal solution of the main problem;
solving the sub-problem based on an interior point method;
if the sub-problem is feasible, obtaining an optimal solution of the alternating current power flow unit combination;
if the sub-problem is not feasible, establishing a relaxation sub-problem of the alternating current power flow unit combination based on the fixed integer variable;
constructing Benders cut constraints according to the relaxor problems;
and adding Benders cut constraint to the main problem to iteratively solve again.
3. The method of claim 1, wherein the main problem comprises a first objective function and first constraints, the first constraints comprising a generator start-up constraint, a generator minimum on-off time constraint, a generator output constraint, a generator rotation standby constraint, a generator ramp-up constraint, a node power balance constraint, an ac power flow equation constraint based on piecewise linear relaxation, and a node voltage safety constraint.
4. The method of claim 1, wherein the sub-problem comprises a second objective function and second constraints, the second constraints comprising generator output constraints, generator rotation standby constraints, generator ramp-up constraints, node power balance constraints, node voltage safety constraints, strict ac power flow equation constraints, and constraints that fix generator set start-stop state variables as the optimal solution to the current main problem.
5. The method of claim 2, wherein the slack sub-problem comprises a third objective function and a third constraint condition, wherein the third constraint condition comprises a generator contribution constraint, a generator rotation standby constraint, a generator ramp-up constraint, a node voltage safety constraint, a strict ac power flow equation constraint, a node power balance constraint introducing slack power, and a constraint fixing a generator set start-stop state variable as an optimal solution to the current main problem.
6. The method of claim 5, wherein constructing Benders cut constraints from the relaxor problem comprises:
obtaining an optimal objective function value of the relaxation sub-problem;
obtaining a Lagrange multiplier corresponding to the constraint that the starting and stopping state variable of the fixed generator set is the optimal solution of the current main problem;
and constructing the Benders cut constraint according to the optimal objective function value and the Lagrangian multiplier.
7. The method according to any of the claims 1 to 6, characterized in that the optimal solution for the AC power flow unit combination comprises the planned start-stop, the supply of rotating reserve, the planned value of active power and the planned value of reactive power of all generators in the future day.
8. A computing device of an alternating current power flow unit combination is characterized by comprising:
the first establishing unit is used for establishing a main problem of the alternating current power flow unit combination based on piecewise linear relaxation;
the second establishing unit is used for establishing a subproblem of the alternating current power flow unit combination based on a fixed integer variable;
and the solving unit is used for solving the main problem and the sub-problems by adopting an alternating iteration algorithm to obtain the optimal solution of the alternating current power flow unit combination.
9. A computer-readable storage medium, characterized in that the computer-readable storage medium includes a stored program, wherein when the program runs, the apparatus on which the computer-readable storage medium is located is controlled to execute the method for calculating the ac power flow unit combination according to any one of claims 1 to 7.
10. A processor, characterized in that the processor is configured to execute a program, wherein the program executes the method for calculating the ac power flow unit combination according to any one of claims 1 to 7.
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