CN110518591B - Load flow calculation method for uncertain power system - Google Patents
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Abstract
The embodiment of the invention provides a load flow calculation method of an uncertain power system, which comprises the following steps: introducing reactive power constraint to PV nodes and balance nodes of an uncertain power system, and constructing a reactive out-of-limit hybrid power flow complementary constraint equation set of the uncertain power system by introducing a given nonlinear function based on the reactive power constraint; defining the active power, the node voltage and the uncertain network parameters of the uncertain power system as interval variables, and respectively expressing the interval variables by using a bounded interval; and solving the hybrid power flow complementary constraint equation set by adopting a given iterative algorithm based on the bounded interval to obtain a voltage change interval of the uncertain power system power flow calculation. The embodiment of the invention can effectively improve the accuracy of load flow calculation of the uncertain power system and effectively improve the convergence.
Description
Technical Field
The invention relates to the technical field of power flow calculation of a power distribution network in a power system, in particular to a power flow calculation method of an uncertain power system.
Background
There are many uncertainties in the operation of the power system, such as the intermittency of the output of new energy plants (e.g. solar energy, wind power plant increase and short term changes), uncertainty of other factors and loads such as weather and electricity prices, and measurement errors of power system network parameters. The uncertain factors can cause the fluctuation, mutation and out-of-limit of the power grid voltage, influence the load flow calculation result of the power system and threaten the safe operation of the power grid.
Currently, load flow calculation methods considering system uncertainty are mainly classified into three categories: (1) a random trend method, namely processing random information by using a probability method; (2) a fuzzy mathematical method, namely establishing a model for power flow calculation of the power distribution network by using fuzzy mathematics, and processing a part of uncertain information by using a fuzzy membership function; (3) and in the interval power flow method, when parameters such as node power, system state and the like cannot be accurately acquired, all variables are expressed as intervals, and finally, an interval expression form of a calculation result is obtained.
However, the above calculation methods (1) and (2) always introduce a certain amount of probability errors, which affect the accuracy of the calculation result, and the method (3) can solve the above problems to some extent, but the reactive power output is controlled by an upper limit and a lower limit, and when the reactive power output is out of limit, the reactive power output can only be maintained at the upper limit or the lower limit, and the node voltage can not be maintained at a set value any more, so that the PV node is changed into a PQ node, the balance node is changed into a Q θ node, and iterative calculation is performed again, and the accuracy still remains, and convergence is seriously affected.
Disclosure of Invention
In order to overcome the above problems or at least partially solve the above problems, embodiments of the present invention provide a method for calculating a power flow of an uncertain power system, so as to effectively improve the accuracy of power flow calculation of the uncertain power system and effectively improve the convergence.
In a first aspect, an embodiment of the present invention provides a method for calculating a power flow of an uncertain power system, including:
introducing reactive power constraint to PV nodes and balance nodes of an uncertain power system, and constructing a hybrid power flow complementary constraint equation set of the uncertain power system with reactive power overrun by introducing a given nonlinear function based on the reactive power constraint and a power flow constraint equation of the uncertain power system;
defining the active power, the node voltage and the uncertain network parameters of the hybrid power flow complementary constraint equation set of the uncertain power system as interval variables, and respectively expressing the interval variables by using a bounded interval;
and solving the hybrid power flow complementary constraint equation set by adopting a given iterative algorithm based on the bounded interval to obtain a voltage change interval of the uncertain power system power flow calculation.
In a second aspect, an embodiment of the present invention provides a power flow calculation apparatus for an uncertain power system, including:
the complementary constraint module is used for introducing reactive power constraint to PV nodes and balance nodes of the uncertain power system, and constructing a hybrid power flow complementary constraint equation set of the uncertain power system during reactive power out-of-limit by introducing a given nonlinear function based on the reactive power constraint and a power flow constraint equation of the uncertain power system;
the interval setting module is used for defining the active power, the node voltage and the uncertain network parameters of the hybrid power flow complementary constraint equation set of the uncertain power system as interval variables, and respectively expressing the interval variables by using bounded intervals;
and the calculation module is used for solving the hybrid power flow complementary constraint equation set by adopting a given iterative algorithm based on the bounded interval to obtain a voltage change interval of the uncertain power system power flow calculation.
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, where the processor executes the computer program to implement the steps of the method for calculating a power flow of an uncertain power system according to the first aspect.
In a fourth aspect, an embodiment of the present invention provides a non-transitory computer readable storage medium, on which computer instructions are stored, and when the computer instructions are executed by a computer, the method for calculating a power flow of an uncertain power system according to the first aspect is implemented.
According to the load flow calculation method of the uncertain power system, provided by the embodiment of the invention, the interval analysis method is adopted, reactive power out-of-limit is processed through complementary constraint, a nonlinear function is introduced, inequality constraint is converted into equality constraint, the load flow calculation accuracy of the uncertain power system can be effectively improved, and the convergence is effectively improved.
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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 flow chart of a method for calculating a power flow of an uncertain power system according to an embodiment of the present invention;
fig. 2 is a schematic flow chart of a method for calculating a power flow of an uncertain power system according to another embodiment of the present invention;
fig. 3 is a schematic structural diagram of a power flow calculation apparatus of an uncertain power system according to an embodiment of the present invention;
fig. 4 is a schematic physical structure 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 obtained by persons of ordinary skill in the art based on the embodiments of the present invention without any creative efforts belong to the protection scope of the embodiments of the present invention.
Aiming at the problem that the accuracy and the convergence are poor when the load flow calculation of the uncertain power system is carried out in the prior art, the embodiment of the invention adopts an interval analysis method, processes reactive power out-of-limit through complementary constraint, introduces a nonlinear function, converts inequality constraint into equality constraint, can effectively improve the accuracy of the load flow calculation of the uncertain power system, and effectively improves the convergence. Embodiments of the present invention will be described and illustrated with reference to various embodiments.
Fig. 1 is a schematic flow chart of a method for calculating a power flow of an uncertain power system according to an embodiment of the present invention, as shown in fig. 1, the method includes:
s101, introducing reactive power constraint to PV nodes and balance nodes of the uncertain power system, and constructing a hybrid power flow complementary constraint equation set of the uncertain power system by introducing a given nonlinear function based on the reactive power constraint and a power flow constraint equation of the uncertain power system.
It can be understood that, in the embodiment of the invention, firstly, aiming at the problem of reactive power out-of-limit of the uncertain power system, the reactive power constraint of the PV node and the balance node is introduced to realize the reactive power compensation of the uncertain power system. Thereafter, a non-linear function is introduced and applied to the reactive power constraint. On the basis, a complementary constraint equation set of the uncertain power system is reconstructed by combining a basic power flow constraint equation of the uncertain power system, namely a hybrid power flow complementary constraint equation set aiming at reactive power out-of-limit.
And S102, defining uncertain network parameters of active power, node voltage and a hybrid power flow complementary constraint equation set of the uncertain power system as interval variables, and respectively expressing the interval variables by using a bounded interval.
The method can be understood as that in consideration of uncertainty of data in the uncertain power system, the embodiment of the invention converts the uncertain power flow problem into a nonlinear interval problem, performs interval setting on the active power, the node voltage of the uncertain power system and uncertain network parameters of a hybrid power flow complementary constraint equation set, and decomposes and solves the nonlinear programming problem by combining the selection theory of the interval extreme values to respectively obtain the upper bound and the lower bound of a real part and an imaginary part of the node voltage in the power flow solution, thereby providing the operating range of the system.
And S103, solving the hybrid power flow complementary constraint equation set by adopting a given iterative algorithm based on the bounded interval to obtain a voltage change interval of the uncertain power system power flow calculation.
It is understood that solving the uncertain power flow equation is to represent variable factors in the uncertain model in the form of intervals, set state variables (such as load voltage, phase angle, generator output) as the intervals, and seek control variables (such as reactive compensation, generator terminal voltage) satisfying the constraint conditions. Specifically, on the basis of the interval setting, the embodiment of the invention adopts an interval analysis method to iteratively solve the obtained hybrid power flow complementary constraint equation set to obtain an interval of uncertain data, such as a voltage change interval.
The load flow calculation method of the uncertain power system provided by the embodiment of the invention is a load flow calculation method based on interval analysis with stronger adaptability, and the load flow calculation method is characterized in that reactive power out-of-limit is processed by using complementary constraint through adopting an interval analysis method, a nonlinear function is introduced, inequality constraint is converted into equality constraint, the accuracy of load flow calculation of the uncertain power system can be effectively improved, and the convergence is effectively improved.
Optionally, according to the above embodiments, the load flow constraint equation of the uncertain power system is as follows:
for the PV node, the node voltage equation is:
in the formula, n represents the number of nodes, ei、fiRepresenting the real and imaginary parts of the voltage, G, at node iij、Bij(i, j) th representing a node admittance matrixComponent, Pi set、Qi setRepresenting constant active and reactive power, U, of node ii setIndicating a voltage control target.
Based on this, the step of introducing reactive power constraints to PV nodes and balance nodes of the uncertain power system specifically includes:
introducing reactive power constraints on PV nodes and balancing nodes as follows:
in the formula, Qi maxAnd Qi minRespectively representing the maximum and minimum values of reactive power at node i, QiRepresenting the actual reactive power at node i.
It can be understood that for the target uncertain power system, a power flow constraint equation of the target uncertain power system in a rectangular coordinate can be constructed. The basic power flow constraint equation may be expressed in the form of a power mismatch, i.e. the power flow constraint equation of the uncertain power system described above. For the PV node, the second of the above-described power flow constraint equations can be replaced with a node voltage equation, namely:
thus, for the PV nodes and the balance nodes, the reactive power constraints are introduced which in turn can be written in the form of a mathematical representation of the reactive power constraints described above.
It is understood that the partitioning of PV nodes, PQ nodes and balance nodes in an uncertain power system is not absolutely constant. The PV node is controlled to a set point voltage primarily because it has an adjustable reactive power output, but its reactive power output is controlled with upper and lower limits, i.e., the node voltage is controlled to a set point voltage
If the reactive power output is out of limit, i.e.
Or
At this time, the reactive power can only be kept at the upper limit value or the lower limit value, the node voltage can not be kept at the set value any more, the PV node is changed into a PQ node, the balance node is changed into a Q theta node, and iterative calculation needs to be carried out again until the limit is not violated. That is, for the PV node and the balance node, the power out-of-range condition needs to be considered, when the reactive power exceeds the limit value, Q takes the maximum value or the minimum value, at this time, the PV node is changed into the PQ node, and iterative calculation needs to be performed again.
In view of this, the embodiment of the present invention optimizes the original reactive complementary constraint. That is, after the step of introducing reactive power constraints to PV nodes and balancing nodes of the uncertain power system, the method of embodiments of the present invention may further comprise: the reactive power constraint is optimized as follows:
in the formula (I), the compound is shown in the specification,
is a relaxation factor introduced, and
correspondingly, a hybrid power flow complementary constraint equation set is constructed based on the power flow constraint equation and the optimized reactive power constraint.
Optionally, according to the above embodiments, the step of constructing the hybrid power flow complementary constraint equation set with uncertain power system reactive power violation by introducing a given nonlinear function specifically includes:
first, a given nonlinear function is introduced as follows:
wherein μ is a relaxation factor.
Secondly, applying a given nonlinear function to reactive power constraint to obtain a reactive power constraint nonlinear equation as follows:
thirdly, based on the power flow constraint equation and the reactive power constraint nonlinear equation, obtaining a hybrid power flow complementary constraint equation set as follows:
it will be appreciated that to solve the problem of complementary constraints, a Fischer-Burmeiter (FB) function is introduced, and that the mixed complementary constraints may be reconstructed using the Fischer-Burmeiter (FB) function, the expression of which is shown above. This function is semi-smooth, can be solved efficiently with the NR method, and can change the search direction smoothly at the constraint exchange cusp, and is therefore more reliable.
It can be understood that, in order to avoid the problem that the FB function (μ, ν) is not differentiable at (0,0), a small value of the relaxation factor μ ═ 10 is introduced-10。
Then, by applying the function φ (μ, v) to the complementary constraints in the power flow calculation, a new equation description can be obtained, i.e. the reactive power constraint nonlinear equation is as above.
And finally, forming a hybrid power flow complementary constraint equation set by using a power flow constraint equation and a reactive power constraint nonlinear equation.
The embodiment of the invention can effectively solve the accuracy problem by introducing the FB function and converting the inequality constraint into the equality constraint condition.
Optionally, according to the above embodiments, the step of defining the uncertain network parameters of the active power, the node voltage, and the hybrid power flow complementary constraint equation set of the uncertain power system as the interval variables specifically includes: regarding the active power as a first interval variable, and defining the fluctuation range of the first interval variable as a first closed interval; and defining the generator node voltage and the uncertain network parameters in the uncertain power system as second interval variables, and uniformly expressing the second interval variables by a second bounded interval.
Specifically, in an uncertain system, the active power P is regarded as a variable in a certain interval, and the possible fluctuation range thereof is defined as a closed interval
Record as
Wherein, PiAnd
respectively the upper and lower bounds of active power. The generator node voltage and the uncertain network parameters are also defined as interval variables, collectively represented by a bounded interval x,
x and
respectively, its lower and upper bounds.
Optionally, in the actual problem calculation, according to the information of load flow calculation for determining the load, the variable range is narrowed to a region near the determined load flow solution, so that the iteration frequency can be reduced, and the calculation efficiency is accelerated. However, if the interval is too large or small, it is difficult to obtain a true interval range solution.
Optionally, according to the above embodiments, the step of solving the hybrid power flow complementary constraint equation system specifically includes: and solving the hybrid power flow complementary constraint equation set by adopting a Gauss-Seidel iterative algorithm or a Krawczyk iterative algorithm. If the mixed power flow complementary constraint equation set is solved by using the Krawczyk iterative algorithm, the iterative formula defining the iterative algorithm is as follows:
wherein the iterative operator
Expressed as:
wherein J (x) represents a Jacobian matrix,
denotes a pre-processing matrix, C denotes a J (x) inverse matrix where x is the center of the interval, I denotes an identity matrix,
represents the rounding-out of x, which represents the generator node voltage and the defined interval of uncertain network parameters.
Specifically, assume a nonlinear system of equations as:
introduction mapping
Then 2N equations can be obtained from the hybrid power flow complementary constraint equation set, and for convenience of expression, the power flow calculation constraint equation can be expressed as:
the solution of the interval nonlinear equation system needs to adopt an iterative method, and the main iterative methods for solving currently include a Newton iterative method and a Krawczyk iterative method. The principle is that when step length is corrected, intersection is taken between the interval of the previous iteration and the iteration operator, and a new interval vector is obtained.
The iterative formula of the iterative method is as follows:
for operator H, the interval Newton operator may be selected:
wherein J (x) is a Jacobian matrix,
indicating an outward rounding of x.
In the iterative algorithm, an inverse matrix of j (x) is required for each step of calculation, but in the case of multivariate, the jacobian matrix is an interval matrix and cannot be directly inverted, so that the iterative algorithm is not a practical method.
In view of this, the embodiment of the present invention uses Gauss-Seidel iterative algorithm or Krawczyk iterative algorithm to solve the interval equation. The embodiment of the invention adopts an improved Krawczyk operator for selecting the operator H, the method is a new iteration form formed by improvement on the basis of a Newton operator, and a non-linear equation system of an interval does not need to be solved in the iteration process, so that matrix inversion operation is avoided, but a reasonable initial iteration interval needs to be selected when the method is used.
For the Krawczyk iterative algorithm, the above iterative formula may be modified as:
thus, the iterative operator
Can be expressed as:
the stop iteration criterion of the Krawczyk algorithm may be set as:
whereinεThe predetermined value is a very small positive number.
To further illustrate the technical solutions of the embodiments of the present invention, the embodiments of the present invention provide the following specific processing flows according to the above embodiments, but do not limit the scope of the embodiments of the present invention.
As shown in fig. 2, a schematic flow chart of a method for calculating a power flow of an uncertain power system according to another embodiment of the present invention includes the following steps:
firstly, according to the equipment running state of the target uncertain power system, establishing a basic power flow constraint equation of the target uncertain power system, and carrying out complementary constraint on the reactive power out-of-limit.
Secondly, in order to solve the inequality problem caused by complementary constraint, a non-linear (Fischer-Burmeiter, FB) function is introduced to obtain a hybrid power flow complementary constraint equation set.
And thirdly, interval setting is carried out on the active power, the node voltage and the like of the target uncertain power system and uncertain network parameters of the hybrid power flow complementary constraint equation set by adopting an interval analysis method.
And finally, on the basis of the interval setting, performing load flow calculation of an uncertain interval on the mixed load flow complementary constraint equation set by adopting a Krawczyk-Moore interval iterative algorithm to obtain a load flow calculation result.
Compared with the prior art, the embodiment of the invention applies an interval analysis method, processes the reactive power out-of-limit problem through complementary constraint, converts inequality constraint into equality constraint by introducing a nonlinear function (Fischer-Burmesiter function, FB function for short), and solves a power flow constraint equation set by using a Krawczyk-Moore interval iterative algorithm, so that the calculation result has higher accuracy and better convergence.
Based on the same concept, the embodiments of the present invention provide a power flow calculation apparatus for an uncertain power system according to the above embodiments, which is used for implementing power flow calculation for the uncertain power system in the above embodiments. Therefore, the description and definition in the load flow calculation method of the uncertain power system in each embodiment may be used for understanding each execution module in the embodiment of the present invention, and specific reference may be made to the above embodiment, which is not described herein again.
According to an embodiment of the present invention, a structure of a power flow calculation apparatus of an uncertain power system is shown in fig. 3, which is a schematic structural diagram of a power flow calculation apparatus of an uncertain power system provided in an embodiment of the present invention, and the apparatus may be used to implement power flow calculation of an uncertain power system in the above method embodiments, and the apparatus includes: a complementary constraint module 301, an interval setting module 302 and a calculation module 303. Wherein:
the complementary constraint module 301 is used for introducing reactive power constraint to PV nodes and balance nodes of the uncertain power system, and constructing a hybrid power flow complementary constraint equation set of the uncertain power system during reactive power out-of-limit by introducing a given nonlinear function based on the reactive power constraint and a power flow constraint equation of the uncertain power system; the interval setting module 302 is configured to define uncertain network parameters of active power, node voltage, and a hybrid power flow complementary constraint equation set of an uncertain power system as interval variables, and respectively represent the interval variables by bounded intervals; the calculation module 303 is configured to solve the hybrid power flow complementary constraint equation set by using a given iterative algorithm based on the bounded interval, and obtain a voltage change interval of the uncertain power system power flow calculation.
Specifically, for the reactive out-of-limit problem of the uncertain power system, the complementary constraint module 301 introduces reactive power constraints of PV nodes and balance nodes to realize reactive compensation of the uncertain power system. The complementary constraint module 301 then introduces a non-linear function and applies the non-linear function to the reactive power constraint. On the basis, the complementary constraint module 301 reconstructs a complementary constraint equation set of the uncertain power system by combining the basic power flow constraint equation of the uncertain power system, namely a hybrid power flow complementary constraint equation set aiming at reactive power out-of-limit.
Then, considering the uncertainty of data in the uncertain power system, the interval setting module 302 converts the uncertainty tide problem into a nonlinear interval problem, performs interval setting on the active power, the node voltage of the uncertain power system and the uncertain network parameters of the hybrid tide complementary constraint equation set, and decomposes and solves the nonlinear programming problem by combining the selection theory of the interval extreme value to obtain the upper bound and the lower bound of the real part and the imaginary part of the node voltage in the tide solution, thereby giving the operating range of the system.
Finally, the calculating module 303 performs iterative solution on the obtained hybrid power flow complementary constraint equation set by using an interval analysis method on the basis of the interval setting, so as to obtain an interval of uncertain data, such as a voltage change interval.
According to the load flow calculation device of the uncertain power system, the corresponding execution module is arranged, the interval analysis method is adopted, reactive power out-of-limit is processed through complementary constraint, the nonlinear function is introduced, the inequality constraint is converted into equality constraint, the accuracy of load flow calculation of the uncertain power system can be effectively improved, and the convergence is effectively improved.
It is understood that, in the embodiment of the present invention, each relevant program module in the apparatus of each of the above embodiments may be implemented by a hardware processor (hardware processor). Moreover, the load flow calculation device of the uncertain power system according to the embodiment of the present invention can implement the load flow calculation process of the uncertain power system according to each method embodiment by using the program modules, and when the load flow calculation device is used for implementing the load flow calculation of the uncertain power system according to each method embodiment, the beneficial effects produced by the device according to the embodiment of the present invention are the same as those of the corresponding method embodiment, and reference may be made to the method embodiments, which are not described herein again.
As a further aspect of the embodiments of the present invention, the present embodiment provides an electronic device according to the above embodiments, where the electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and when the processor executes the computer program, the method implements the steps of the method for calculating the power flow of the uncertain power system according to the above embodiments.
Further, the electronic device of the embodiment of the present invention may further include a communication interface and a bus. Referring to fig. 4, an entity structure diagram of an electronic device provided in an embodiment of the present invention includes: at least one memory 401, at least one processor 402, a communication interface 403, and a bus 404.
The memory 401, the processor 402 and the communication interface 403 complete mutual communication through the bus 404, and the communication interface 403 is used for information transmission between the electronic device and the target uncertain power system data device; the memory 401 stores a computer program operable on the processor 402, and the processor 402 executes the computer program to implement the steps of the method for calculating the power flow of the uncertain power system according to the embodiments described above.
It is understood that the electronic device at least includes a memory 401, a processor 402, a communication interface 403 and a bus 404, and the memory 401, the processor 402 and the communication interface 403 are connected in communication with each other through the bus 404, and can perform communication with each other, for example, the processor 402 reads program instructions of a power flow calculation method of an uncertain power system from the memory 401. In addition, the communication interface 403 may also implement communication connection between the electronic device and the target uncertain power system data device, and may complete mutual information transmission, such as reading of power system data through the communication interface 403.
When the electronic device is running, the processor 402 calls the program instructions in the memory 401 to perform the methods provided by the above-mentioned method embodiments, including for example: introducing reactive power constraint to PV nodes and balance nodes of the uncertain power system, and constructing a hybrid power flow complementary constraint equation set of the uncertain power system during reactive power out-of-limit by introducing a given nonlinear function based on the reactive power constraint and a power flow constraint equation of the uncertain power system; defining the active power, the node voltage and the uncertain network parameters of the hybrid power flow complementary constraint equation set of the uncertain power system as interval variables, and respectively expressing the interval variables by using bounded intervals; and solving the hybrid power flow complementary constraint equation set by adopting a given iterative algorithm based on the bounded interval to obtain a voltage change interval and the like of the uncertain power system power flow calculation.
The program instructions in the memory 401 may be implemented in the form of software functional units and stored in a computer readable storage medium when sold or used as a stand-alone product. Alternatively, all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, where the program may be stored in a computer-readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
Embodiments of the present invention further provide a non-transitory computer readable storage medium according to the above embodiments, on which computer instructions are stored, and when the computer instructions are executed by a computer, the method for calculating a power flow of an uncertain power system according to the above embodiments is implemented, for example, the method includes: introducing reactive power constraint to PV nodes and balance nodes of the uncertain power system, and constructing a hybrid power flow complementary constraint equation set of the uncertain power system during reactive power out-of-limit by introducing a given nonlinear function based on the reactive power constraint and a power flow constraint equation of the uncertain power system; defining the active power, the node voltage and the uncertain network parameters of the hybrid power flow complementary constraint equation set of the uncertain power system as interval variables, and respectively expressing the interval variables by using bounded intervals; and solving the hybrid power flow complementary constraint equation set by adopting a given iterative algorithm based on the bounded interval to obtain a voltage change interval and the like of the uncertain power system power flow calculation.
According to the electronic device and the non-transitory computer readable storage medium provided by the embodiments of the present invention, by executing the steps of the load flow calculation method of the uncertain power system described in each of the above embodiments, an interval analysis method is adopted, reactive power violations are processed through complementary constraints, a non-linear function is introduced, and an inequality constraint is converted into an equality constraint, so that the accuracy of load flow calculation of the uncertain power system can be effectively improved, and the convergence can be effectively improved.
It is to be understood that the above-described embodiments of the apparatus, the electronic device and the storage medium are merely illustrative, and that elements described as separate components may or may not be physically separate, may be located in one place, or may be distributed on different network elements. Some or all of the modules can be selected according to actual needs to achieve the purpose of the scheme of the 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. Based on such understanding, the technical solutions mentioned above may be embodied in the form of a software product, which may be stored in a computer-readable storage medium, such as a usb disk, a removable hard disk, a ROM, a RAM, a magnetic or optical disk, etc., and includes several instructions for causing a computer device (such as a personal computer, a server, or a network device, etc.) to execute the methods described in the method embodiments or some parts of the method embodiments.
In addition, it should be understood by those skilled in the art that in the specification of the embodiments of the present invention, 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 a process, method, article, or apparatus that comprises the element.
In the description of the embodiments of the invention, numerous specific details are set forth. It is understood, however, that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description. Similarly, it should be appreciated that in the foregoing description of exemplary embodiments of the invention, various features of the embodiments of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects.
However, the disclosed method should not be interpreted as reflecting an intention that: that is, the claimed embodiments of the invention require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of an embodiment of this invention.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the embodiments of the present invention, and not to limit the same; although embodiments of the present invention have been described in detail with reference to the foregoing embodiments, it should be understood by those skilled 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 the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (9)
1. A load flow calculation method of an uncertain power system is characterized by comprising the following steps:
introducing reactive power constraint to PV nodes and balance nodes of an uncertain power system, and constructing a hybrid power flow complementary constraint equation set of the uncertain power system with reactive power overrun by introducing a given nonlinear function based on the reactive power constraint and a power flow constraint equation of the uncertain power system;
defining the active power, the node voltage and the uncertain network parameters of the hybrid power flow complementary constraint equation set of the uncertain power system as interval variables, and respectively expressing the interval variables by using a bounded interval;
solving the hybrid power flow complementary constraint equation set by adopting a given iterative algorithm based on the bounded interval to obtain a voltage change interval of the uncertain power system power flow calculation;
the solving of the hybrid power flow complementary constraint equation set by adopting a given iterative algorithm comprises the following steps:
and solving the hybrid power flow complementary constraint equation set by adopting a Gauss-Seidel iterative algorithm or a Krawczyk iterative algorithm.
2. The method for calculating the power flow of the uncertain power system as claimed in claim 1, wherein the power flow constraint equation of the uncertain power system is as follows:
for the PV node, the node voltage equation is:
in the formula, n represents the number of nodes, ei、fiRepresenting the real and imaginary parts of the voltage, G, at node iij、BijRepresenting the (i, j) th component, P, of the nodal admittance matrixi set、Qi setRepresenting constant active and reactive power, U, of node ii setRepresents a voltage control target;
the step of introducing reactive power constraints to PV nodes and balance nodes of the uncertain power system specifically comprises the following steps:
introducing reactive power constraints to the PV nodes and the balance nodes as follows:
in the formula, Qi maxAnd Qi minRespectively representing the maximum and minimum values of reactive power at node i, QiRepresenting the actual reactive power at node i.
3. The method for calculating power flow of an uncertain power system as claimed in claim 2, wherein the step of constructing the hybrid power flow complementary constraint equation set for reactive power violation of the uncertain power system by introducing a given nonlinear function specifically comprises:
the given nonlinear function is introduced as follows:
wherein mu is a relaxation factor;
applying the given nonlinear function to the reactive power constraint to obtain a reactive power constraint nonlinear equation as follows:
in the formula (I), the compound is shown in the specification,
is a relaxation factor introduced, and
based on the power flow constraint equation and the reactive power constraint nonlinear equation, the hybrid power flow complementary constraint equation set is obtained as follows:
4. the method for calculating power flow of an uncertain power system according to any of claims 1 to 3, wherein the step of defining the active power, the node voltage of the uncertain power system and the uncertain network parameters of the hybrid power flow complementary constraint equation set as interval variables specifically comprises:
regarding the active power as a first interval variable, and defining the fluctuation range of the first interval variable as a first closed interval;
and defining the generator node voltage in the uncertain power system and the uncertain network parameters as second interval variables, and uniformly expressing the second interval variables by a second bounded interval.
5. The method of load flow calculation for an indeterminate power system as claimed in claim 2, further comprising, after said step of introducing reactive power constraints on PV nodes and balancing nodes of the indeterminate power system:
optimizing the reactive power constraint according to:
in the formula (I), the compound is shown in the specification,
is a relaxation factor introduced, and
correspondingly, the hybrid power flow complementary constraint equation set is constructed based on the power flow constraint equation and the optimized reactive power constraint.
6. The method for calculating the power flow of the uncertain power system as recited in claim 1, wherein if the mixed power flow complementary constraint equation set is solved by using a Krawczyk iterative algorithm, an iterative formula defining the iterative algorithm is as follows:
wherein the iterative operator
Expressed as:
wherein J (x) represents a Jacobian matrix,
denotes a pre-processing matrix, C denotes a J (x) inverse matrix where x is the center of the interval, I denotes an identity matrix,
represents the rounding-out of x, which represents the generator node voltage and the defined interval of uncertain network parameters.
7. A power flow calculation apparatus for an indeterminate power system, comprising:
the complementary constraint module is used for introducing reactive power constraint to PV nodes and balance nodes of the uncertain power system, and constructing a hybrid power flow complementary constraint equation set of the uncertain power system during reactive power out-of-limit by introducing a given nonlinear function based on the reactive power constraint and a power flow constraint equation of the uncertain power system;
the interval setting module is used for defining the active power, the node voltage and the uncertain network parameters of the hybrid power flow complementary constraint equation set of the uncertain power system as interval variables, and respectively expressing the interval variables by using bounded intervals;
the calculation module is used for solving the hybrid power flow complementary constraint equation set by adopting a given iterative algorithm based on the bounded interval to obtain a voltage change interval of the uncertain power system power flow calculation;
the solving of the hybrid power flow complementary constraint equation set by adopting a given iterative algorithm comprises the following steps:
and solving the hybrid power flow complementary constraint equation set by adopting a Gauss-Seidel iterative algorithm or a Krawczyk iterative algorithm.
8. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor, when executing the computer program, implements the steps of the method for calculating a power flow of an uncertain power system as claimed in any of claims 1 to 6.
9. A non-transitory computer readable storage medium having stored thereon computer instructions, wherein the computer instructions, when executed by a computer, implement the steps of the method for calculating a power flow of an uncertain power system as claimed in any of claims 1 to 6.
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