CN112269967A - Iteration splitting method and system based on joint opportunity constraint - Google Patents

Iteration splitting method and system based on joint opportunity constraint Download PDF

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CN112269967A
CN112269967A CN202011096837.2A CN202011096837A CN112269967A CN 112269967 A CN112269967 A CN 112269967A CN 202011096837 A CN202011096837 A CN 202011096837A CN 112269967 A CN112269967 A CN 112269967A
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沈沉
贾孟硕
陈颖
黄少伟
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Abstract

The embodiment of the invention provides an iterative splitting method and system based on joint opportunity constraint, wherein the method comprises the following steps: establishing an optimization model containing opportunity constraint, and determining constraint conditions of the optimization model containing opportunity constraint; and splitting the joint opportunity constraint in the constraint condition based on an iteration splitting framework to obtain the single event probability and the random event combination probability. The embodiment of the invention is used for splitting the joint probability into the single event probability and the random event combination probability approximately equivalently by accurately estimating the random event combination probability, thereby reducing the conservative property of the joint opportunity constraint split.

Description

Iteration splitting method and system based on joint opportunity constraint
Technical Field
The invention relates to the technical field of power systems, in particular to an iterative splitting method and system based on joint opportunity constraint.
Background
In the power system, a random optimization model considering joint opportunity constraint can provide stronger safety guarantee so as to deal with uncertainty caused by renewable energy sources. However, since the joint opportunity constraint is strongly nonlinear and non-convex, no algorithm can directly obtain the global optimal solution of the optimization problem with the joint opportunity constraint at present. The joint opportunity constraint is split into the single opportunity constraint, and then the single opportunity constraint is converted into the deterministic constraint by using quantile conversion, so that the method is an effective solution for solving the optimization problem containing the joint opportunity constraint. The key to this technique is how to split the joint opportunity constraint into single opportunity constraints.
The existing splitting algorithms directly use Boolean inequality to split the probability of a combined event into the sum of the probabilities of a plurality of single events, and then divide the equally-divided risk threshold or the optimized risk threshold into each single event to form single opportunity constraint. However, the probability of a joint event is not equivalent to the sum of the single event probabilities, but is equal to the sum of the single event probabilities minus the joint event cross term probability. In other words, the probability of a joint event is much less than the sum of the probabilities of the individual events. Therefore, existing splitting algorithms will introduce a lot of conservatism, resulting in a final solution that is only sub-optimal.
In order to solve the problem, the prior art proposes an estimation algorithm, that is, the probability of all events occurring simultaneously is estimated by using samples, so that the probability of the combined event is converted into the sum of the probabilities of the single events minus the probability of all events occurring simultaneously, and the conservatism is reduced. Further, the prior art provides an improved estimation algorithm, which tries to estimate the probability of simultaneous occurrence of any event combination by using samples, and further converts the probability of a joint event into the sum of the probabilities of single events minus the probability of simultaneous occurrence of all event combinations, thereby further reducing the conservatism. However, the true probability of the event occurrence is essentially determined by the optimal solution of the original problem, and the true event occurrence probability can be estimated only if the optimal solution of the original problem is obtained. However, it is only possible to obtain the optimal solution of the original problem by obtaining the probability of the true event occurrence. This is a logical dilemma of the typical "whether there are previous chickens or eggs". Neither of the above algorithms takes this key problem into account, but instead uses artificially generated samples for estimation. This may result in incompatibility between the estimation result and the subsequent so-called "optimal solution", and overestimation and even contradiction occur, so that the joint opportunity constraint cannot be satisfied, and the security of the system corresponding to the joint opportunity constraint cannot be ensured.
Therefore, there is a need for an iterative splitting method and system based on joint opportunity constraint to solve the above problems.
Disclosure of Invention
Aiming at the problems in the prior art, the embodiment of the invention provides an iterative splitting method and system based on joint opportunity constraint.
In a first aspect, an embodiment of the present invention provides an iterative splitting method based on joint opportunity constraint, including:
establishing an optimization model containing opportunity constraint, and determining constraint conditions of the optimization model containing opportunity constraint;
and splitting the joint opportunity constraint in the constraint condition based on an iteration splitting framework to obtain the single event probability and the random event combination probability.
Further, the objective function of the optimization model with opportunity constraint is as follows:
Figure BDA0002724037080000024
wherein, gtAnd the output of the schedulable unit at the time t is shown.
Further, the constraint conditions include a unit capacity constraint, a climbing constraint, a power balance constraint and a line capacity constraint, wherein the line capacity constraint is a joint opportunity constraint.
Further, the joint opportunity constraint is:
Figure BDA0002724037080000021
wherein litRepresenting the power flow of line i at time t,
Figure BDA0002724037080000022
and
Figure BDA0002724037080000023
upper and lower bounds, sets, respectively representing power flows of line i
Figure BDA0002724037080000025
Representing the line set of interest.
Further, the splitting the joint opportunity constraint in the constraint condition based on the iterative splitting framework to obtain a single event probability and an arbitrary event combination probability includes:
generating a wind power sample at each moment;
pre-solving the target function based on a Boolean inequality to obtain a conservative solution;
substituting the wind power sample and the conservative solution into a line power flow, and estimating the out-of-limit probability of a single event;
sequentially estimating the combined probability of any event;
and (4) solving again by using the newly split single opportunity constraint until the change of the objective function is stopped.
Further, the method further comprises:
in the iterative splitting process, the risk threshold corresponding to the single opportunity constraint is adjusted based on a self-adaptive risk threshold allocation mechanism.
Further, the adjusting the risk threshold corresponding to the single opportunity constraint based on the adaptive risk threshold apportionment mechanism includes:
Figure BDA0002724037080000031
wherein the content of the first and second substances,
Figure BDA0002724037080000032
representing the out-of-limit probability of a single event.
In a second aspect, an embodiment of the present invention provides an iterative splitting system based on joint opportunity constraint, including:
the model establishing module is used for establishing an optimization model containing opportunity constraint and determining the constraint conditions of the optimization model containing opportunity constraint;
and the iteration splitting module is used for splitting the joint opportunity constraint in the constraint condition based on an iteration splitting framework to obtain the single event probability and the random event combination probability.
In a third aspect, an embodiment of the present invention provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the method provided in the first aspect when executing the program.
In a fourth aspect, an embodiment of the present invention provides a non-transitory computer readable storage medium, on which a computer program is stored, which when executed by a processor, implements the steps of the method as provided in the first aspect.
The iterative splitting method and the iterative splitting system based on the joint opportunity constraint, provided by the embodiment of the invention, are used for splitting the joint probability into the single event probability and the random event combination probability approximately equivalently by accurately estimating the random event combination probability, so that the conservative property of the joint opportunity constraint splitting is reduced.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
Fig. 1 is a schematic flowchart of an iterative splitting method based on joint opportunity constraint according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of an iterative splitting system based on joint opportunity constraint according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. 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 invention.
Fig. 1 is a schematic flow diagram of an iterative splitting method based on joint opportunity constraint according to an embodiment of the present invention, and as shown in fig. 1, an embodiment of the present invention provides an iterative splitting method based on joint opportunity constraint, including:
step 101, establishing an optimization model containing opportunity constraint, and determining constraint conditions of the optimization model containing opportunity constraint;
and 102, splitting the joint opportunity constraint in the constraint condition based on an iterative splitting framework to obtain the single event probability and the random event combination probability.
In the embodiment of the invention, an optimization model containing opportunity constraint is established by taking the minimization of the power generation cost in multiple periods as a target, wherein the constraint condition can be determined. The constraint conditions comprise unit capacity constraint, climbing constraint, power balance constraint and line capacity constraint, wherein the line capacity constraint is joint opportunity constraint. It should be noted that, in the embodiment of the present invention, the first three sets of constraints are all linear constraints, and are independent of the joint opportunity constraint, and the final line capacity constraint is the joint opportunity constraint.
Further, in step 102, the embodiment of the present invention splits the joint constraint based on the iterative splitting framework to split the joint probability into a single event probability and an arbitrary event combination probability approximately equivalently, thereby reducing the conservative property of the joint constraint split.
The iterative splitting method based on the joint opportunity constraint provided by the embodiment of the invention is used for splitting the joint probability into the single event probability and the arbitrary event combination probability approximately equivalently by accurately estimating the arbitrary event combination probability, so that the conservative property of the joint opportunity constraint splitting is reduced.
On the basis of the above embodiment, the objective function of the optimization model with opportunity constraint is to minimize the power generation cost in multiple periods as the objective of the optimization model:
Figure BDA0002724037080000059
wherein, gtAnd the output of the schedulable unit at the time t is shown.
On the basis of the above embodiment, the joint opportunity constraint is:
Figure BDA0002724037080000051
wherein litRepresenting the power flow of line i at time t,
Figure BDA0002724037080000052
and
Figure BDA0002724037080000053
upper and lower bounds, sets, respectively representing power flows of line i
Figure BDA00027240370800000510
Representing the line set of interest.
In the embodiment of the invention, the meaning of the joint opportunity constraint formula is set
Figure BDA00027240370800000511
The probability that the power flow of all lines in the system does not exceed the upper and lower bounds is greater than 1-alpha, where alpha is often a relatively small value, such as 5%.
By using the linear power flow model, the power flow l of the line i at the time t can be obtaineditRepresented by the formula:
Figure BDA0002724037080000054
wherein, wtRepresenting the output of the wind power at the moment t which cannot be scheduled, dtIndicating the load at time t. Coefficient of performance
Figure BDA0002724037080000055
And
Figure BDA0002724037080000056
are the mapping coefficients between the corresponding power injection and the line power flow. Wind power may be further characterized by predicted values and prediction errors:
Figure BDA0002724037080000057
wherein the content of the first and second substances,
Figure BDA0002724037080000058
representing the predicted value of the output of the wind power at the moment t, deltatIndicating the prediction error. Obviously, the prediction error is a random variable, which in turn leads to litRandomness is also included.
On the basis of the above embodiment, the splitting the joint opportunity constraint in the constraint condition based on the iterative splitting framework to obtain a single event probability and an arbitrary event combination probability includes:
generating a wind power sample at each moment;
pre-solving the target function based on a Boolean inequality to obtain a conservative solution;
substituting the wind power sample and the conservative solution into a line power flow, and estimating the out-of-limit probability of a single event;
sequentially estimating the combined probability of any event;
and (4) solving again by using the newly split single opportunity constraint until the change of the objective function is stopped.
In the embodiment of the present invention, it is,
Figure BDA0002724037080000061
is provided with
Figure BDA0002724037080000062
A single constraint, the out-of-limit condition for each single constraint, can be characterized as event yn：
Figure BDA0002724037080000063
Wherein the content of the first and second substances,
Figure BDA0002724037080000064
and xnIs represented byitOr-lit，
Figure BDA0002724037080000065
Then represent correspondingly
Figure BDA0002724037080000066
Or
Figure BDA0002724037080000067
In practice, not every single constraint may be out of bounds, i.e., there are y's that are unlikely to happenn. Defining a set of events that may occur as
Figure BDA0002724037080000068
Then there are:
Figure BDA0002724037080000069
the last term in the above formula can be expressed according to inclusion-exclusion rules
Figure BDA00027240370800000610
Further development, namely:
Figure BDA00027240370800000611
where E represents the integration of the joint probabilities of all possible event combinations. Thus, the formula
Figure BDA00027240370800000612
Is equivalent to:
Figure BDA00027240370800000613
once the collection is known
Figure BDA00027240370800000614
And the value E can be estimated, and then combined with a risk apportionment mechanism, the joint opportunity constraint can be split into single opportunity constraints:
Figure BDA0002724037080000071
wherein, betanRepresenting a risk-sharing factor. Further, an iterative splitting framework is constructed, which focuses on how to accurately obtain the set
Figure BDA0002724037080000072
How to estimate E accurately, and how to design betanThereby eliminating nearly the conservation of joint opportunity constraint splits.
The specific iteration splitting framework is as follows:
step S11, sample generation: for each time instant, N is generatedsA wind power sample, each sample being represented as
Figure BDA0002724037080000073
Where s is 1, …, Ns；
Step S12, pre-solving: the original problem is pre-solved using the traditional boolean inequality to obtain a conservative solution, denoted as
Figure BDA0002724037080000074
Step S13, classification: will be provided with
Figure BDA0002724037080000075
And
Figure BDA0002724037080000076
substituting into line power flow to generate NsLine flow samples, i.e.
Figure BDA0002724037080000077
The out-of-limit probability of a single event is then estimated using the following equation:
Figure BDA0002724037080000078
wherein if a>And f (a) is 0, then f (a) is 1, otherwise f (a) is 0.
Figure BDA0002724037080000079
Event indexes corresponding to more than 0 constitute a set
Figure BDA00027240370800000710
Step S14, estimating: definition set
Figure BDA00027240370800000711
Characterizing any combination of events, the corresponding event index constituting a vector xsThe upper bound of the event constitutes the vector x+Then set
Figure BDA00027240370800000712
The probability of the event in (1) occurring simultaneously is:
Figure BDA00027240370800000713
then, the probabilities of any event combination can be estimated in sequence and then summed to obtain E;
step S15, adaptive risk allocation: in the iterative splitting process, based on an adaptive risk threshold value apportionment mechanism, adjusting a risk threshold value corresponding to a single opportunity constraint, wherein an adaptive risk apportionment factor is defined as follows:
Figure BDA00027240370800000714
wherein the content of the first and second substances,
Figure BDA00027240370800000715
representing the out-of-limit probability of a single event. Then, according to the formula
Figure BDA00027240370800000716
Figure BDA00027240370800000717
The joint opportunity constraint is split into a single opportunity constraint. Obviously each time obtaining
Figure BDA0002724037080000081
Thereafter, the risk threshold corresponding to each single opportunity constraint is dynamically adjusted. At the same time, the user can select the desired position,
Figure BDA0002724037080000082
the large value indicates that the single constraint is easy to exceed the limit, and the corresponding risk threshold value is large, so that more adjustment spaces are obtained; on the contrary, the present invention is not limited to the above-described embodiments,
Figure BDA0002724037080000083
a small value indicates that this single constraint is difficult to override and the corresponding risk threshold becomes small, thereby saving unnecessary real estate.
Step S16, repeatedly solving: and solving the optimization problem again by using the newly split single opportunity constraint. After obtaining the optimal solution, updating
Figure BDA0002724037080000084
And repeats steps S13 through S16 until the change in the objective function can be ignored.
Need attention toIs, in the embodiment of the present invention, since the sets
Figure BDA0002724037080000085
And the probability value E are based on the latest
Figure BDA0002724037080000086
Therefore, the current real situation can be reflected best. When in use
Figure BDA0002724037080000087
After stabilization, assemble
Figure BDA0002724037080000088
And the probability value E will also be stable, so the final set
Figure BDA0002724037080000089
And the probability value E are both accurate values, and final
Figure BDA00027240370800000810
And correspondingly.
The embodiment of the invention provides a self-adaptive risk threshold value allocation mechanism, and conservatism caused by splitting is further reduced, so that introduced conservatism can be ignored.
Fig. 2 is a schematic structural diagram of an iterative splitting system based on joint opportunity constraint according to an embodiment of the present invention, and as shown in fig. 2, an embodiment of the present invention provides an iterative splitting system based on joint opportunity constraint, which includes a model establishing module 201 and an iterative splitting module 202, where the model establishing module 201 is configured to establish an optimization model including opportunity constraint and determine a constraint condition of the optimization model including opportunity constraint; the iteration splitting module 202 is configured to split the joint opportunity constraint in the constraint condition based on an iteration splitting framework to obtain a single event probability and an arbitrary event combination probability.
The iterative splitting system based on the joint opportunity constraint provided by the embodiment of the invention is used for splitting the joint probability into the single event probability and the random event combination probability approximately equivalently by accurately estimating the random event combination probability, so that the conservative property of the joint opportunity constraint splitting is reduced.
The system provided by the embodiment of the present invention is used for executing the above method embodiments, and for details of the process and the details, reference is made to the above embodiments, which are not described herein again.
Fig. 3 is a schematic structural diagram of an electronic device according to an embodiment of the present invention, and referring to fig. 3, the electronic device may include: a processor (processor)301, a communication Interface (communication Interface)302, a memory (memory)303 and a communication bus 304, wherein the processor 301, the communication Interface 302 and the memory 303 complete communication with each other through the communication bus 304. Processor 301 may call logic instructions in memory 303 to perform the following method: establishing an optimization model containing opportunity constraint, and determining constraint conditions of the optimization model containing opportunity constraint; and splitting the joint opportunity constraint in the constraint condition based on an iteration splitting framework to obtain the single event probability and the random event combination probability.
In addition, the logic instructions in the memory 303 may be implemented in the form of software functional units and stored in a computer readable storage medium when the logic instructions are sold or used as independent products. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
In another aspect, an embodiment of the present invention further provides a non-transitory computer-readable storage medium, on which a computer program is stored, where the computer program is implemented by a processor to perform the joint opportunity constraint-based iterative splitting method provided in the foregoing embodiments, for example, including: establishing an optimization model containing opportunity constraint, and determining constraint conditions of the optimization model containing opportunity constraint; and splitting the joint opportunity constraint in the constraint condition based on an iteration splitting framework to obtain the single event probability and the random event combination probability.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. An iterative splitting method based on joint opportunity constraint is characterized by comprising the following steps:
establishing an optimization model containing opportunity constraint, and determining constraint conditions of the optimization model containing opportunity constraint;
and splitting the joint opportunity constraint in the constraint condition based on an iteration splitting framework to obtain the single event probability and the random event combination probability.
2. The iterative splitting method based on joint opportunity constraints of claim 1, wherein the objective function of the optimization model with opportunity constraints is:
Figure FDA0002724037070000011
wherein, gtAnd the output of the schedulable unit at the time t is shown.
3. The iterative splitting method based on joint opportunity constraints according to claim 2, wherein the constraint conditions include a unit capacity constraint, a hill climbing constraint, a power balance constraint and a line capacity constraint, wherein the line capacity constraint is a joint opportunity constraint.
4. The iterative splitting method based on joint opportunity constraint of claim 3, wherein the joint opportunity constraint is:
Figure FDA0002724037070000012
wherein litRepresenting the power flow of line i at time t,
Figure FDA0002724037070000013
and
Figure FDA0002724037070000014
upper and lower bounds, sets, respectively representing power flows of line i
Figure FDA0002724037070000015
Representing the line set of interest.
5. The iterative splitting method based on joint opportunity constraint according to claim 4, wherein the splitting the joint opportunity constraint in the constraint condition based on the iterative splitting framework to obtain a single event probability and an arbitrary event combination probability comprises:
generating a wind power sample at each moment;
pre-solving the target function based on a Boolean inequality to obtain a conservative solution;
substituting the wind power sample and the conservative solution into a line power flow, and estimating the out-of-limit probability of a single event;
sequentially estimating the combined probability of any event;
and (4) solving again by using the newly split single opportunity constraint until the change of the objective function is stopped.
6. The iterative splitting method based on joint opportunity constraints of claim 5, further comprising:
in the iterative splitting process, the risk threshold corresponding to the single opportunity constraint is adjusted based on a self-adaptive risk threshold allocation mechanism.
7. The iterative splitting method based on joint opportunity constraints according to claim 6, wherein the adjusting the risk threshold corresponding to a single opportunity constraint based on an adaptive risk threshold apportionment mechanism comprises:
Figure FDA0002724037070000021
wherein the content of the first and second substances,
Figure FDA0002724037070000022
representing the out-of-limit probability of a single event.
8. An iterative splitting system based on joint opportunity constraints, comprising:
the model establishing module is used for establishing an optimization model containing opportunity constraint and determining the constraint conditions of the optimization model containing opportunity constraint;
and the iteration splitting module is used for splitting the joint opportunity constraint in the constraint condition based on an iteration splitting framework to obtain the single event probability and the random event combination probability.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the program implements the steps of the joint opportunity constraint based iterative splitting method of any one of claims 1 to 7.
10. A non-transitory computer readable storage medium having stored thereon a computer program, which when executed by a processor implements the steps of the iterative splitting method based on joint opportunity constraints as recited in any one of claims 1 to 7.
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