CN109193809B - Sensitivity matrix-based power system active safety correction optimization method - Google Patents
Sensitivity matrix-based power system active safety correction optimization method Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
- H02J3/48—Controlling the sharing of the in-phase component
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Abstract
The invention discloses a sensitivity matrix-based power system active safety correction optimization method, which comprises the steps of firstly analyzing the specific requirements of safety correction problems according to the application scene of safety correction; then, according to the specific requirements of the safety correction problem, introducing a 0-1 variable and a continuous variable analysis expression adjustment equipment number and an equipment adjustment quantity, and constructing a safety correction multi-objective optimization model; secondly, weighting different magnitudes on the load nodes and the generator nodes, and simultaneously converting a multi-objective optimization problem into a single-objective optimization problem by adopting a maximum value method; then, introducing an intermediate variable to eliminate an absolute value item in the target function, analyzing a constraint condition of a safety correction problem, and expressing the constraint condition by using a sensitivity matrix; and finally, solving by adopting a branch-and-bound method (DICOPT solver of GAMS (optimization software)). The invention can effectively make up the defects of the traditional sensitivity safety correction method, effectively reduce the number of devices involved in correction and the adjustment amount, and improve the rationality of the load shedding scheme.
Description
Technical Field
The invention relates to a sensitivity matrix-based power system active safety correction optimization method, and belongs to the technical field of power system correlation.
Background
The power system active safety correction eliminates the overload condition of the system by means of adjusting the output of the generator and reducing the load. In the traditional sensitivity class method for safety correction, adding and subtracting power nodes are determined according to the sensitivity of the node active injection power to the branch active power, the adding and subtracting power nodes are sorted according to the absolute value of the sensitivity, and then a pair of adding and subtracting power nodes (control node groups) are sequentially selected according to the sorting result and are adjusted until the threshold is eliminated.
In order to maintain the power balance of the system, each pair of control node groups always obeys the principle of reverse equivalent pairing in the adjusting process, namely the adjustment amount of each pair of adding and subtracting power nodes is equal. Therefore, when there is a node with a small adjustable amount in some control node group with higher sensitivity, the adjustment capability of the control node group cannot be effectively exerted. And the sensitivity method is adjusted in a mode of artificially formulating an adjustment rule, so that the obtained scheduling scheme is difficult to achieve the optimal state, the number of devices participating in adjustment is too large, and the adjustment amount of the system is too large.
Although the prior art combines sensitivity with optimization methods, the main sequence of adjustment is still in the order of sensitivity magnitude, and therefore, the advantages of the optimization methods are not well exploited.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a power system active safety correction optimization method based on a sensitivity matrix aiming at the defects related in the background technology, effectively combine the respective advantages of a sensitivity method and an optimization method, and improve the rationality and the high efficiency of an adjustment scheme.
The invention adopts the following technical scheme for solving the technical problems:
the invention provides a sensitivity matrix-based power system active safety correction optimization method, which comprises the following steps:
the method comprises the following steps:
step 1), analyzing specific requirements of safety correction problems according to an application scene of active safety correction of a power system;
step 2), according to the specific requirements of the safety correction problem, introducing a 0-1 variable and a continuous variable analysis expression to adjust the number of equipment and the equipment adjustment quantity, and constructing a safety correction multi-objective optimization model;
step 3), weighting different magnitudes on the load node and the generator node, and simultaneously converting the multi-objective optimization model in the step 2) into a single-objective optimization model by adopting a maximum value method;
step 4), introducing an intermediate variable to simplify the single-target optimization model in the step 3), analyzing the constraint condition of the single-target optimization model, and expressing the constraint condition by using a sensitivity matrix;
and 5) solving the optimization model obtained in the step 4) by adopting a branch-and-bound method to obtain the optimal solution of the safety correction problem, thereby completing the correction and optimization of the active safety of the electric power system.
As a further technical solution of the present invention, in the step 1), the specific requirement for safety correction problem includes two aspects: determining the minimum number of nodes involved in adjustment under the condition of meeting various constraints of a system; and selecting an adjusting scheme with the least equipment adjusting amount under the condition of the minimum adjusting node number.
As a further technical solution of the present invention, in the step 2), the safety correction multi-objective optimization model includes:
adjusting the objective function with the least number of nodes:
the objective function with the least amount of equipment adjustment:
in the formula, i is a node number; n isbThe number of nodes that are systems; 0-1 variable biCharacterizing the adjustment status of node i, diAnd characterizing the active adjustment quantity of the node i.
As a further technical solution of the present invention, in the step 3), an objective function of the single-objective optimization model is:
in the formula, WiIndicating node i adjustment status biThe weight of (c); wi *Indicating node i active adjustment diThe weight of (c); m is a maximum.
As a further technical solution of the present invention, in the step 4), the single-objective optimization model in the step 3) is simplified by introducing an intermediate variable to obtain:
in the formula (d)i1And di2Is notA negative intermediate variable;
the constraint conditions are as follows:
wherein M' is a very small number;
representing the initial active power on the line i,
is the thermal stability limit of line l;
the lower limit of the active injection for node i,
representing the initial active injection of node i,
an upper limit for active injection for node i; sliThe sensitivity coefficient of the line l to the node i is the ith row and ith column element in the sensitivity matrix S of the system.
As a further technical scheme of the invention, the sensitivity of the node injection power to the line active power is utilized to express the system power change, and a direct current model is adopted to describe the sensitivity of the node to the branch circuit:
S＝B'AB-1
wherein B' is a diagonal matrix consisting of branch admittances; b is a square matrix formed by imaginary parts of the node admittance matrixes; a is a branch-node association matrix of the network; s is the sensitivity matrix of the system.
As a further technical scheme of the invention, when the node i is connected with a generator, WiIs 1, Wi *Is 0.01; when there is no generator on node i, WiIs 100, Wi *Is 1; of MValue of 10-6。
As a further technical scheme of the invention, a DICOPT solver of the optimization software GAMS is adopted for solving in the step 5).
Compared with the prior art, the invention adopting the technical scheme has the following technical effects: according to the invention, the target function with the minimum number of adjusting equipment and the minimum adjusting quantity is analyzed and expressed by introducing the forms of 0-1 variable and continuous variable, various constraint conditions required to be met in the correction process are expressed based on the sensitivity matrix, and the advantages of simplicity in solving by using a sensitivity method and capability of obtaining an optimal solution by using an optimization method are efficiently combined. Meanwhile, the invention eliminates the absolute value part in the adjustment quantity function by introducing intermediate variables and increasing constraints, thereby effectively improving the solving efficiency of the model. In addition, the invention limits the adjustable load of each node, and effectively improves the rationality of the load shedding scheme. In conclusion, the invention can rapidly eliminate the overload condition in the system, avoid the occurrence of load shedding action as much as possible and reduce the economic loss caused by safety correction.
Detailed Description
The following detailed description of embodiments of the invention is intended to be illustrative, but not limiting, of the invention.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The technical scheme of the invention is further explained in detail by combining the specific examples as follows:
a power system active power safety correction optimization method based on a sensitivity matrix comprises the following steps:
step 1), analyzing specific requirements of safety correction problems according to an application scene of active safety correction of a power system;
step 2), according to the specific requirements of the safety correction problem, introducing a 0-1 variable and a continuous variable analysis expression to adjust the number of equipment and the equipment adjustment quantity, and constructing a safety correction multi-objective optimization model;
step 3), weighting different magnitudes on the load node and the generator node, and simultaneously converting the multi-objective optimization model in the step 2) into a single-objective optimization model by adopting a maximum value method;
step 4), introducing an intermediate variable to eliminate an absolute value item in the objective function of the single-target optimization model in the step 3), analyzing the constraint condition of the single-target optimization model, and expressing the constraint condition by using a sensitivity matrix;
and 5) solving the optimization model obtained in the step 4) by adopting a branch-and-bound method (a DICOPT solver of optimization software GAMS) to obtain an optimal solution of the safety correction problem, so that the correction and optimization of the active safety of the power system are completed.
Further, in the step 1), the safety correction of the power system is mostly carried out when the system fails and the line is overloaded, and the overload condition in the system is eliminated by means of adjusting the output of the generator and reducing the load; in order to ensure that the system is quickly restored to a safe operation state, the adjusting equipment involved in the correction process is required to be as small as possible, and the adjusting amount of the equipment is also required to be as small as possible, so that the overload condition in the system can be quickly eliminated; therefore, it has the following two requirements for the adjustment scheme: (1) the number of nodes involved in the adjustment is sufficiently small; (2) when the number of nodes involved in the adjustment is sufficiently small, the amount of power adjustment of the nodes is reduced as much as possible. Therefore, solving the above problem in an optimization method involves two layers: determining the minimum number of nodes involved in adjustment under the condition of meeting various constraints of a system; secondly, because multiple adjustment schemes may exist under the minimum adjustment node number, the power adjustment quantity of the nodes needs to be optimized continuously on the basis of the first step, and therefore a group of schemes with the minimum adjustment quantity is selected.
Further, in the step 2), according to the requirement of safety correction problem, in the correction processThe invention aims to ensure that related adjusting equipment is small enough and the adjusting quantity of the equipment is small enough, so that the invention expresses the active safety correction problem as a multi-objective optimization problem which aims at the minimum number of the adjusting equipment and the minimum system adjusting quantity, wherein the number of the adjusting equipment is the main aim; in order to analytically express the number of adjusting devices and the adjusting amount, the invention introduces a variable b of 0-1iCharacterizing the adjustment state of a node i, wherein 0 represents that the node is not involved in the adjustment, and 1 represents that the node is involved in the adjustment; at the same time, a variable d is introducediAnd respectively representing the active adjustment quantity of the node i. Therefore, the objective function that adjusts the minimum number of nodes is:
the objective function with the least amount of equipment adjustment is:
in the formula, i is a node number; n isbIs the number of nodes of the system.
Further, in the step 3), during the safety correction process, the generator node participates in the adjustment in the form of adjusting the output of the generator, and the load node participates in the adjustment in the form of load shedding. In order to ensure a certain economic benefit, the load cutting action is avoided as much as possible, and the load cutting amount is reduced as much as possible. For this purpose, the invention assigns the generator node and the load node with weights of different magnitudes, and assigns f1And f2Modified into3And f4：
In the formula (I), the compound is shown in the specification,Wia weight representing the adjustment state of node i; wi *And representing the weight of the active adjustment quantity of the node i. In order to ensure that the generator node is preferentially adjusted in the correction process, the adjustment cost of the load node is far greater than that of the generator node, and for this reason, the weight of the adjustment state of the generator node is selected to be 1, and the weight of the adjustment state of the load node is selected to be 100. Meanwhile, the cost of the load adjustment amount is far larger than that of the generator adjustment amount, and in order to avoid the influence on the adjustment amount part, the weight of the load adjustment amount is 1, and the weight of the generator adjustment amount is 0.01.
Because the complaint of the safety correction problem is to further optimize the adjustment amount on the basis of preferentially determining the minimum number of adjustment nodes, the invention introduces a maximum value M (the value of the maximum value M is 1000) to f3And f4Are combined into f5Therefore, the multi-objective problem is converted into a single-objective optimization problem, the complexity of the model is reduced, and the solving efficiency of the model is improved; due to the existence of the maximum value M, the number of nodes participating in adjustment can be preferentially determined in the solving process, and then the adjustment amount of the system is optimized, so that the requirement of a safety correction problem can be met:
further, in the step 4), since the target function has an absolute value term, the solving difficulty of the model is greatly increased, and therefore, the non-negative intermediate variable d is introduced into the methodi1And di2To f5Modifying, and eliminating an absolute value item in the target function, wherein the modified target function is as follows:
to ensure di1+di2Can reduce | diThe value of | the present invention adds the following constraints to the model:
due to the inclusion of the equilibrium constraint di1di2For 0, the constraint makes its derivative function not meet continuous conductibility, which can bring challenge to model solving to a certain extent, for this reason, the invention relaxes the constraint and converts it into di1di2M 'is less than or equal to M', wherein M 'is a very small number, and the value of the M' is 10-6。
Because a variable of 0-1 is introduced, the difficulty in solving the problem is increased, and the traditional nonlinear power balance equation is not beneficial to model solution, therefore, the invention expresses the power change of the system by utilizing the sensitivity of the node injection power to the active power of the line, and adopts a direct current model to describe the sensitivity of the node to the branch circuit:
S＝B'AB-1
wherein B' is a diagonal matrix consisting of branch admittances; b is a square matrix formed by imaginary parts of the node admittance matrixes; a is a branch-node association matrix of the network; s is a sensitivity matrix of the system, which describes the relationship between the line active power flow and the node injection power; element S thereofliThe sensitivity coefficient of the line l to the node i represents that the active power flow variation of the branch l is S when the active injection on the node i changes the unit valueli；
Therefore, in addition to the relevant constraints of the intermediate variables, the safety correction problem should also satisfy the following constraints:
wherein, the 1 st bar represents that the active power of the adjusted line l is smaller than the allowable thermal stability limit value, in the formula,
representing the initial active power on the line i,
is the thermal stability limit of line l; the bar 2 represents that the power balance of the system is maintained in the adjusting process, and the active injection increased by all the nodes is equal to the active injection reduced by all the nodes; bar 3 indicates that the adjustment of the node is to meet its limit, where,
representing the initial active injection of the node i, the value of which is the difference value of the initial output of the generator and the initial load of the node,P ifor the lower limit of the active injection of the node i, the value of the node is 0 for the generator node, and for the load node, in order to avoid influencing important loads, the value of the node is 30% of the opposite number of the absolute value of the active load carried by the node (namely 30% of non-important loads on the node i can be cut off and can be set according to actual conditions),
the upper limit of active power injection of the node i is defined, the value of the node of the generator is the maximum output allowed by the generator, and the value of the node of the load is 0; bar 4 sub-representation biIs a variable from 0 to 1.
As can be seen from the bar 3, when biWhen the value is 1, the node i participates in regulation, and the upper limit of the active injection power of the node is
The lower limit isP iThus, the amount d of adjustment thereofiIs not 0; when b isiWhen the value is 0, the node i does not participate in regulation, and the upper limit and the lower limit of the active injection power are both
Thus, the amount d is adjustedPiIs always 0; the processing mode can avoid the condition that the node does not participate in adjustment and the adjustment quantity is not 0 in the solving process, thereby effectively ensuring the accuracy of the model.
Further, in the step 5), a branch-and-bound method (DICOPT solver of the optimization software GAMS) is adopted for solving, and an optimal solution of the security correction problem is obtained.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.
Claims (5)
1. A power system active power safety correction optimization method based on a sensitivity matrix is characterized by comprising the following steps:
step 1), analyzing specific requirements of safety correction problems according to an application scene of active safety correction of a power system;
step 2), according to the specific requirements of the safety correction problem, introducing a 0-1 variable and a continuous variable analysis expression to adjust the number of equipment and the equipment adjustment quantity, and constructing a safety correction multi-objective optimization model; the safety correction multi-objective optimization model comprises the following steps:
adjusting the objective function with the least number of nodes:
the objective function with the least amount of equipment adjustment:
in the formula, i is a node number; n isbThe number of nodes that are systems; 0-1 variable biCharacterizing the adjustment status of node i, diRepresenting the active adjustment quantity of the node i;
step 3), weighting different magnitudes on the load node and the generator node, and simultaneously converting the multi-objective optimization model in the step 2) into a single-objective optimization model by adopting a maximum value method; the objective function of the single-target optimization model is as follows:
in the formula, WiIndicating node i adjustment status biThe weight of (c); wi *Indicating node i active adjustment diThe weight of (c); m is a maximum number;
step 4), introducing a non-negative intermediate variable to simplify the single-target optimization model in the step 3), analyzing the constraint condition of the single-target optimization model, and expressing the constraint condition by using a sensitivity matrix; wherein, introducing non-negative intermediate variables to simplify the single-target optimization model in step 3) to obtain:
in the formula (d)i1And di2Is a non-negative intermediate variable;
the constraint conditions are as follows:
wherein M' is a very small number; pl 0Representing the initial active power on the line i,
is the thermal stability limit of line l;P ifor the lower limit of active injection, P, of node ii 0Representing the initial active injection of node i,
an upper limit for active injection for node i; sliThe sensitivity coefficient of the line l to the node i is the ith row element in the sensitivity matrix S of the system;
and 5) solving the optimization model obtained in the step 4) by adopting a branch-and-bound method to obtain the optimal solution of the safety correction problem, thereby completing the correction and optimization of the active safety of the electric power system.
2. The method for optimizing the active safety correction of the power system based on the sensitivity matrix as claimed in claim 1, wherein in the step 1), the specific requirements of the safety correction problem include two aspects: determining the minimum number of nodes involved in adjustment under the condition of meeting various constraints of a system; and selecting an adjusting scheme with the least equipment adjusting amount under the condition of the minimum adjusting node number.
3. The active safety correction optimization method of the power system based on the sensitivity matrix according to claim 1, characterized in that the sensitivity of the node injection power to the line active power is used to express the system power change, and a direct current model is used to describe the sensitivity of the node to the branch:
S＝B'AB-1
wherein B' is a diagonal matrix consisting of branch admittances; b is a square matrix formed by imaginary parts of the node admittance matrixes; a is a branch-node association matrix of the network; s is the sensitivity matrix of the system.
4. The power system active safety correction optimization method based on the sensitivity matrix as claimed in claim 1, wherein when node i is connected with a generator, W isiIs 1, Wi *Is 0.01; when there is no generator on node i, WiIs 100, Wi *Is 1; m' has a value of 10-6。
5. The method for optimizing the active safety correction of the power system based on the sensitivity matrix as claimed in claim 1, wherein the step 5) is performed by using a DICOPT solver of optimization software GAMS.
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