A power system power flow calculation method and system

Abstract

The application discloses a power system power flow calculation method and system, aiming at the problem that the wide range change of the operation mode in the new power system causes the difficulty in giving the output of part of generators and node voltage, and relaxes the key variables such as the output of part of generators and node voltage from the equality constraint to the inequality constraint; after introducing the inequality constraint, the power flow model is changed from the original nonlinear equation set solving problem to the constraint power flow model of the new power system; the method of constructing an auxiliary function is adopted to convert the inequality in the constraint power flow model into an equality, and then the constraint power flow model is converted into a least square problem with bounded constraints; aiming at the problem that the traditional optimization algorithm is difficult to converge, the trust region algorithm is adopted to solve, and the adjustment amount of the variables such as the output of the generator and the node voltage and the final power flow solution are obtained. The method can effectively solve the problem that the power flow has no solution due to the difficulty in giving the initial value of the power flow, and provides theoretical support for the planning and operation of the power system.

Description

Technical Field

[0001] This invention belongs to the field of power system power flow calculation technology, specifically relating to a power system power flow calculation method and system. Background Technology

[0002] Given a network topology and load, our research has consistently focused on finding a reasonable start-up mode for the power system by rationally configuring generator output and the switching of related equipment, thereby enabling the power system to operate efficiently, economically, and reliably. By reasonably specifying generator output and voltage, and then evaluating parameters such as voltage, phase angle, and current at each node in the power system through power flow calculations, we determine whether a solution exists if the power flow has a solution. If no solution exists, we seek parameter adjustment measures, such as adjusting generator output, reactive power compensation equipment, and transformer tap changes, to achieve power flow convergence and thus obtain a reasonable operating mode.

[0003] New power systems introduce fluctuating power sources such as photovoltaic and wind power, integrate battery energy storage into the grid, and employ numerous power electronic devices including DC transmission, flexible AC transmission, and load control. These developments lead to significant changes in the structure and operation of the power system. Traditional power flow models and algorithms struggle to fully describe these new characteristics, necessitating a rethinking and optimization of power flow calculation methods.

[0004] The increasing proportion of fluctuating power sources such as solar and wind power, coupled with the grid integration of these sources, introduces uncertainties and time-varying characteristics, leading to a significant diversification and increasing complexity in power system operation. Traditional power flow models and calculation methods are no longer adequate for solving these new power systems. Therefore, in order to adapt to the operating characteristics of these new power systems, in-depth research and improvement of power flow models and algorithms are crucial.

[0005] New power systems incorporate numerous power electronic devices, such as inverters and converters, to enable grid connection of photovoltaic, wind power generation, and battery energy storage, as well as DC transmission. The presence of these devices complicates power flow calculation models, rendering traditional transmission line parameter-based methods inadequate for accurately describing system operation. The nonlinear characteristics of power electronic devices and the complexity of their control strategies necessitate more refined modeling and solution methods for analysis and optimization. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a power flow calculation method and system to address the shortcomings of the prior art, thereby solving the technical problem that the initial value of the power flow is difficult to give, which leads to the lack of a solution for the power flow, and improving the situation where the traditional power flow convergence is difficult or even fails in the new power system.

[0007] The present invention adopts the following technical solution:

[0008] A method for calculating power flow in a power system includes the following steps:

[0009] Establish a new power flow constraint model;

[0010] The inequalities in the new power-constrained power flow model are transformed into equations by constructing auxiliary functions.

[0011] Transform the equation into a bounded least squares problem;

[0012] The trust region method is used to solve the least squares problem, and the adjustment amounts of variables such as generator output and node voltage in the power system are obtained, as well as the final power flow solution.

[0013] Preferably, in the novel power flow constraint model, the equality constraint is expressed as:

[0014]

[0015] Inequality constraints in a constrained power flow model are expressed as:

[0016]

[0017]

[0018] x l ≤x≤x u

[0019] Where N represents the set of all nodes, A represents the set of nodes with relaxed generator active power output, B represents the set of nodes with relaxed generator reactive power output, and C represents the set of nodes with relaxed node voltage amplitude; for node i, e i a represents the real part of the voltage. i f represents the real part of the current. i b represents the imaginary part of the voltage. i P represents the imaginary part of the current. Li P represents the active power absorbed by the load. Gi Q represents the active power generated by the generator. Li Q represents the reactive power absorbed by the load. Gi This indicates the reactive power output of the generator. x represents the given voltage amplitude.l Denotes the lower bound of the iteration variable, x u G represents the upper bound of the iteration variable. ij B represents the real part of the nodal admittance matrix. ij This represents the real part of the nodal admittance matrix.

[0020] Preferably, the inequalities in the novel power constraint power flow model are transformed into equations as follows:

[0021] The constrained power flow model is transformed into a system of nonlinear inequalities and nonlinear equations under standard bounded constraints, where the bilateral constraints of the upper and lower bounds are transformed into two unilateral constraints.

[0022] Construct a penalty function to convert inequalities into equality.

[0023] Preferably, the penalty function is constructed as follows:

[0024] Based on the concept of penalty functions, an auxiliary function for continuously differentiable functions is constructed. By adding a penalty term related to the degree of constraint violation to the objective function, the value of the objective function increases when the constraint is violated.

[0025] Preferably, transforming the equation into a bounded least squares problem specifically involves:

[0026] Based on the construction of an auxiliary function, firstly, according to the input equation vector C E And inequality vector C I Form the vector function h and its corresponding Jacobian matrix J0;

[0027] Then, the vector function h and its corresponding Jacobian matrix J0 are corrected according to the constructed auxiliary function to obtain F and its corresponding Jacobian matrix J.

[0028] Preferably, the bounded least squares problem is as follows:

[0029]

[0030] Where x is the iteration variable, l is the lower bound of the iteration variable, u is the upper bound of the iteration variable, F(x) is the power flow equation system after the inequalities are transformed into equations, and f(x) is the objective function.

[0031] Preferably, the block representation of vector functions h and J0 is as follows:

[0032] h = [C E C I ] T =[h e1 h e2 h i1 h i2 h i3h i4 h i5 ] T

[0033] J0 = [J 0e1 J 0e2 J 0i1 J 0i2 J 0i3 J 0i4 J 0i5 ] T

[0034] Among them, h e J represents an equality vector; e h e The corresponding Jacobian matrix; h i J represents the inequality vector; i h i The corresponding Jacobian matrix;

[0035] h e and h i All elements in the equation are determined by voltage deviation ΔU 2 Active power deviation ΔP, reactive power deviation ΔQ, lower limit voltage deviation Lower boundary active power deviation ΔP l Lower boundary reactive power deviation ΔQ l Upper limit voltage deviation Upper boundary active power deviation ΔP u Upper limit reactive power deviation ΔQ u composition;

[0036] There are 2n1 equation constraints for the active power deviation ΔP and reactive power deviation ΔQ at node PQ. The vector function h and the corresponding Jacobian matrix J, represented in blocks, are as follows:

[0037]

[0038]

[0039] There are a total of n²-m¹ equality constraints for the active power deviation ΔP at node P. The vector function h and the corresponding Jacobian matrix J, represented in blocks, are as follows:

[0040]

[0041]

[0042] Lower bound voltage magnitude inequality constraint at PQ node and upper limit voltage magnitude inequality constraint There are a total of 2n1 vector functions, and the corresponding Jacobian matrix J are represented as follows:

[0043]

[0044]

[0045] Lower bound active power deviation ΔP of the node l Deviation of active power from upper limit ΔP u There are a total of 2m1 inequality constraints, and the vector function h and the corresponding Jacobian matrix J are represented in block form as follows:

[0046]

[0047]

[0048] P node and Lower bound reactive power deviation ΔQ of the node l The reactive power deviation ΔQ from the upper limit u There are a total of 2n² inequality constraints. The vector function h and the corresponding Jacobian matrix J, represented in blocks, are as follows:

[0049]

[0050]

[0051] P node and Node lower bound voltage magnitude inequality constraint and upper limit voltage magnitude inequality constraint There are a total of 2n² vector functions, and the corresponding Jacobian matrix J is represented as follows:

[0052]

[0053]

[0054] The lower bound active power deviation ΔP at node Vθ l Lower boundary reactive power deviation ΔQ l Upper boundary active power deviation ΔP u Upper limit reactive power deviation ΔQ u There are four in total. The vector function h and the corresponding Jacobian matrix J, represented in block form, are as follows:

[0055] h i5 =[ΔP l,n ΔP u,n ΔQ l,n ΔQ u,n ] T

[0056]

[0057] Preferably, the gradient corresponding to f is:

[0058]

[0059] in, J is the gradient of the objective function f. T Let F be the transpose of the Jacobian matrix of the power flow equation vector F after the inequality is transformed into an equation, where F is the power flow equation vector after the inequality is transformed into an equation.

[0060] Preferably, the modification of the vector function h and its corresponding Jacobian matrix J0 is specifically as follows:

[0061] F = h

[0062] ee

[0063] F i =[h i ] +

[0064] J e =J 0e

[0065] (J i ) i =max{(h i ) i ,0}(J 0i ) i

[0066] Among them, F e h is the vector of the power flow equation after the inequality is transformed into an equation. e Let F be the vector of the power flow equation. i h is the vector of the power flow inequality equations after the inequality is transformed into an equality. i Let J be the vector of the power flow inequality equation. e J is the Jacobian matrix of the power flow equation vectors after the inequality is transformed into an equation. 0e J is the Jacobian matrix of the vectors in the power flow equation. i is the Jacobian matrix of the power flow inequality equation vector after the inequality is transformed into an equality.

[0067] Secondly, embodiments of the present invention provide a power system power flow calculation system, comprising:

[0068] Build modules to establish a new power constraint power flow model;

[0069] The first transformation module uses the method of constructing auxiliary functions to transform the inequalities in the obtained new power constraint power flow model into equal equations;

[0070] The second transformation module transforms the equations into bounded least squares problems;

[0071] The calculation module uses the trust region method to solve the least squares problem, obtaining the adjustment amounts of variables such as generator output and node voltage in the power system, as well as the final power flow solution.

[0072] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the power system power flow calculation method described above.

[0073] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described power system power flow calculation method.

[0074] Fifthly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the power system power flow calculation method described above.

[0075] In a sixth aspect, embodiments of the present invention provide an electronic device including a computer program, which, when executed by the electronic device, implements the steps of the above-described power system power flow calculation method.

[0076] Compared with the prior art, the present invention has at least the following beneficial effects:

[0077] A new power flow calculation method for power systems expands the solution space and convergence region of the power flow by using slack variables, thus resolving ill-conditioned power flow problems that were previously unconvergenceable by the Newton-Raphson algorithm. For cases where the power flow has no solution, a mechanism is used to obtain a reasonable operating mode by infinitely relaxing generator output. Compared to traditional power flow, constrained power flow requires fewer known quantities and can expand the solution space, thus effectively addressing situations where generator output and voltage amplitude are difficult to determine in the calculation of power flow in new power systems. Constrained power flow requires fewer known quantities than traditional power flow; for values ​​that are difficult to determine in traditional power flow, we only need to specify a range. Based on the three node types in traditional power flow, six new node types are added, allowing for flexible setting of known and unknown quantities. Furthermore, by applying reasonable constraints to the slack variables, the solution process is ensured to progress towards the desired result, avoiding the unsatisfactory results after convergence in traditional power flow calculations, thereby enabling a more efficient operation of the power system.

[0078] Furthermore, the advantages of transforming the equations into bounded least squares problems are as follows: firstly, restricting each variable to a specific range serves as a specification for the mapping domain; secondly, restricting the iterative variables to the feasible region prevents infeasible iteration points located outside the feasible region or infeasible iteration directions from arising during the iteration process; and thirdly, converting all single-variable simple bound constraints into equations and placing them in the objective function would result in a very large dimensional objective function, leading to a decrease in computational efficiency. Therefore, we only convert inequality constraints into equations and place them in the objective function, while retaining the simple bound constraints of the variables.

[0079] Furthermore, based on the mathematical model of the constrained power flow model, the trust region algorithm is used for solution. Compared with Newton's method, the trust region algorithm has higher robustness. For ill-conditioned problems that are difficult to solve by Newton's method, the trust region algorithm may converge to a reasonable solution. At the same time, the trust region algorithm can solve well-posed, underdetermined, and overdetermined problems, thus allowing for flexible setting of node types. This invention provides mathematical analytical expressions and corresponding iterative formats for the power flow model under different conditions. Examples demonstrate that the trust region algorithm has good computational efficiency and robustness.

[0080] It is understandable that the beneficial effects of the second aspect mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0081] In summary, this invention provides a novel model and algorithm for power flow calculation in power systems. It is worth noting whether the proposed method can effectively address the problems of difficult or even failed convergence of traditional power flow methods.

[0082] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0083] Figure 1 This is a flowchart illustrating the overall implementation of the method of the present invention;

[0084] Figure 2 This is a flowchart illustrating the specific implementation of the trust region algorithm in solving the constrained power flow model of a new type of power system.

[0085] Figure 3 A schematic diagram illustrating the basic idea of ​​the trust region algorithm;

[0086] Figure 4 A schematic diagram illustrating the expansion of the solution space by slack variables in a constrained power flow model;

[0087] Figure 5 To obtain constrained power flow models and algorithm systems for new power system operation modes;

[0088] Figure 6 A schematic diagram of a computer device provided in an embodiment of the present invention;

[0089] Figure 7 This is a block diagram of a chip provided according to an embodiment of the present invention. Detailed Implementation

[0090] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0091] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0092] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0093] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0094] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0095] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0096] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0097] This invention provides a method for calculating power flow in power systems. Based on the traditional power flow model, it relaxes the generator output of some generator nodes and applies constraints based on the actual system. Simultaneously, it constrains the voltage amplitude of nodes without a given voltage amplitude, resulting in a novel constrained power flow model. The constrained power flow model is transformed into a least-squares problem and solved using the trust-region algorithm. The specific transformation method and the trust-region algorithm solution process are provided. The results of this research are expected to provide some theoretical guidance for novel power flow calculations.

[0098] Please see Figure 1 The present invention provides a power system power flow calculation method, comprising the following steps:

[0099] S1. Establish a new power constraint power flow model;

[0100] To address the problem that the output of some generators and the voltage of nodes are difficult to determine due to the large-scale changes in the operating modes of new power systems, the key variables such as the output of some generators and the voltage of nodes are relaxed from equality constraints to inequality constraints. After introducing inequality constraints, the power flow model changes from solving the original nonlinear equation system to a constrained power flow model for new power systems.

[0101] In response to the problem that the introduction of fluctuating power sources, DC transmission, and power electronics technology in new power systems makes it difficult to give initial values ​​in traditional power flow models and algorithms, or makes it difficult for power flow algorithms to converge when initial values ​​are forcibly given, this invention studies and researches constrained power flow models.

[0102] There are three main scenarios for trend calculation: benign trend, pathological trend, and trend with no solution.

[0103] For benign currents, it is desirable for the current calculation to converge quickly;

[0104] For ill-conditioned power flow, it is hoped that the constrained power flow model can expand the solution space of the power flow and converge to a feasible solution;

[0105] In cases where there is no solution for the power flow, the constrained power flow model can expand the solution space by infinitely relaxing the generator output, thereby enabling the power flow to converge. Based on the convergence result and the degree of the infinitely relaxed generator's out-of-bounds behavior, the load size, generator output, and reactive power compensation equipment configuration can be appropriately adjusted to bring the power flow solution back to the feasible region.

[0106] In new power systems, the power output of wind and solar power sources and the node voltage and active power output of some generator nodes in DC transmission systems cannot be given. Therefore, based on the traditional power flow algorithm, the requirements are relaxed, and only a range is given relative to the given constant value. In order to prevent the voltage amplitude from being too high or too low in the power flow result, resulting in unqualified voltage quality, or the generator output exceeding the limit and obtaining an infeasible solution that does not conform to the actual system, the relevant state variables are constrained according to the actual system. In this way, the solution obtained is sure to be a feasible solution.

[0107] Based on the traditional power flow model, the generator output of some generator nodes is relaxed and constraints are applied based on the actual system. At the same time, the voltage amplitude of nodes without given voltage amplitude is constrained, thus obtaining a new power system constrained power flow model.

[0108] It is noted that there are three types of nodes in the traditional power flow model: PQ nodes, PV nodes, and slack nodes. Since the voltage of each node is unknown before the power flow calculation, the active and reactive power losses cannot be determined. The active and reactive power outputs of the slack nodes are not given. Since Newton's method cannot solve the problem of inequality constraints, the output of the slack generator is not constrained. Instead, after the power flow converges, the power flow solution is judged to be within the feasible region based on whether the output of the slack node generator exceeds the limit. That is, the slack node in the traditional power flow model is equivalent to the infinitely relaxed generator node in the constrained power flow model.

[0109] In constrained power flow models, there are multiple relaxed generator nodes, so there is no concept of a slack node. The Vθ node in a constrained power flow model no longer represents the concept of a slack node, but only refers to a voltage reference node with given voltage magnitude and phase angle.

[0110] In other words, this invention relaxes the voltage amplitude of all nodes except the Vθ node, selectively relaxes the active power output of some PV nodes, and relaxes the reactive power output of all PV nodes.

[0111] Therefore, based on the three node types in traditional power flow models—PQ nodes, PV nodes, and Vθ nodes—constrained power flow models have expanded to include new node types: P nodes, Q nodes, V nodes, QV nodes, and PQV nodes. The nodes, where P, Q, U, and θ are all undetermined, are used in the constrained power flow model of the new power system. There are multiple relaxed generators, so there is no longer a concept of a balancing machine in the constrained power flow model. The Vθ node only represents the voltage reference node with given voltage amplitude and voltage phase.

[0112] The specific node numbering settings of this invention are shown in the table below:

[0113] Table 1 Node Numbering Settings

[0114]

[0115] Under the above node numbers, the iteration variables are:

[0116] x = [e1, f1, ..., e n-1 ,f n-1 ] T (1)

[0117] After relaxing some variables, constraints are applied to ensure that the relaxed variables do not exceed the limits in the power flow calculation results. Thus, the traditional power flow model consisting of a system of nonlinear inequalities is transformed into a constrained power flow model consisting of nonlinear equality and nonlinear inequality equations.

[0118] The equality constraints in the constrained power flow model are then expressed as:

[0119]

[0120] Inequality constraints in a constrained power flow model are expressed as:

[0121]

[0122]

[0123] x l ≤x≤x u

[0124] Where N represents the set of all nodes, A represents the set of nodes with relaxed generator active power output, B represents the set of nodes with relaxed generator reactive power output, and C represents the set of nodes with relaxed node voltage amplitude.

[0125] S2. The inequalities in the new power constraint power flow model obtained in step S1 are transformed into equal equations by constructing auxiliary functions.

[0126] Constrained power flow models are essentially composed of a series of equations containing nonlinear equality and nonlinear inequality. Numerical optimization theory is typically used to solve such systems of equations. Therefore, the inequalities must first be transformed into equality, and then the system of nonlinear equality and nonlinear inequality equations in the constrained power flow model must be transformed into a least-squares problem with bounded constraints for efficient solution.

[0127] S201. Transform the constrained power flow model into a system of nonlinear inequalities and nonlinear equations under standard bounded constraints, where the bilateral constraints of the upper and lower bounds are transformed into two unilateral constraints.

[0128] S202. Based on two commonly used transformation methods, inequalities are converted into equations, thereby transforming the problem of solving nonlinear inequalities and nonlinear equation systems into a bounded least squares problem represented by the following formula, so as to facilitate the solution using numerical optimization algorithms.

[0129]

[0130] First, the constrained power flow model is standardized as follows:

[0131]

[0132] Among them, the bilateral constraints of the upper and lower bounds are transformed into two unilateral constraints, both of which are expressed in the form of less than 0.

[0133] use Represents an equality vector. Let L represent the inequality vector, L represent the lower bound vector of the variable, and U represent the upper bound vector of the variable. Therefore, equation (6) can be expressed as:

[0134]

[0135] For constrained power flow models, C E and C I All are continuously differentiable. To transform equation (7) into a least squares problem, two methods are used: introducing slack variables and constructing a penalty function.

[0136] The first approach is to introduce additional slack variables s to transform the inequalities into equalities, and then add appropriate boundary constraints.

[0137] Specifically, for (7), a nonnegative slack variable should be introduced. The nonnegativity of s is determined by the inequality constraints. The iterative variable in the least squares problem is then x = (v...). T ,s T ) T , It is given by the following formula:

[0138]

[0139] As can be seen, the core idea of ​​adding slack variables is to transfer the "inequality sign" of the inequality to the variable, thus transforming nonlinear inequalities and systems of equations into systems of equations with simple variable constraints.

[0140] The biggest advantage of constructing least squares problems by adding slack variables is that the objective function is relatively simple, thus simplifying the calculation of the Jacobian matrix during iteration. However, this algorithm also has its drawbacks, as adding slack variables increases the dimensionality of the iteration variables, which can increase the computational cost to some extent.

[0141] Besides adding slack variables, another common transformation method is to construct an auxiliary function for the continuously differentiable function, as follows:

[0142] [t] + =max{t,0} 2 / 2 (9)

[0143] At this point, the iteration variable x = v T , It is given by the following formula:

[0144]

[0145] When c i When (x)≤0, [c i (v)] + It equals 0, therefore for If the contribution is 0, it will cause f(x) to move toward 0;

[0146] Conversely, when c i When (x)>0, [c i (v)] + A value greater than zero will give F(x) a positive component, causing f(x) to move in the direction of increasing, that is, moving away from 0.

[0147] Conversely, constructing continuously differentiable functions also has advantages and disadvantages compared to adding slack variables.

[0148] First, constructing the auxiliary function does not require adding extra variables, thus reducing the number of iteration variables that need to be solved during the iteration process. However, the construction of the auxiliary function, F(x) and its corresponding Jacobian matrix, is relatively more complex, which also increases the computational load to some extent.

[0149] S3. Transform the equation obtained in step S2 into a bounded least squares problem.

[0150] The two algorithms for converting inequalities into equality in step S2 have similar computational complexity. This invention uses the algorithm for constructing auxiliary functions as an example to illustrate the process of establishing the least squares problem.

[0151] During the iteration process, the formation of the objective function and the Jacobian matrix is ​​crucial. This invention, based on the construction of an auxiliary function, first determines the objective function and the Jacobian matrix based on the input equality vector C. EAnd inequality vector C I Form a vector function h and its corresponding Jacobian matrix J0; then modify the vector function h and its corresponding Jacobian matrix J0 according to the constructed auxiliary function to obtain F and its corresponding Jacobian matrix J.

[0152] The block representation of vector functions h and J0 in this invention is shown in formulas (11) and (12):

[0153] h = [C E C I ] T =[h e1 h e2 h i1 h i2 h i3 h i4 h i5 ] T (11)

[0154] J0 = [J 0e1 J 0e2 J 0i1 J 0i2 J 0i3 J 0i4 J 0i5 ] T (12)

[0155] Among them, h e J represents an equality vector; e h e The corresponding Jacobian matrix; h i J represents the inequality vector; i h i The corresponding Jacobian matrix.

[0156] h e and h i All elements in the equation are determined by voltage deviation ΔU 2 Active power deviation ΔP, reactive power deviation ΔQ, lower limit voltage deviation Lower boundary active power deviation ΔP l Lower boundary reactive power deviation ΔQ l Upper limit voltage deviation Upper boundary active power deviation ΔP u Upper limit reactive power deviation ΔQ u The matrix is ​​divided into blocks for ease of programming and modification.

[0157] 1) There are 2n1 equation constraints for the active power deviation ΔP and reactive power deviation ΔQ at nodes P and Q. The vector function h and the corresponding Jacobian matrix J, represented in blocks, are as follows:

[0158]

[0159]

[0160] 2) There are a total of n²-m¹ equation constraints for the active power deviation ΔP at node P. The vector function h and the corresponding Jacobian matrix J, represented in blocks, are as follows:

[0161]

[0162]

[0163] 3) Lower bound voltage magnitude inequality constraint at PQ node and upper limit voltage magnitude inequality constraint There are a total of 2n1 vector functions, and the corresponding Jacobian matrix J are represented as follows:

[0164]

[0165]

[0166] 4) Lower bound active power deviation ΔP of the node l Deviation of active power from upper limit ΔP u There are a total of 2m1 inequality constraints, and the vector function h and the corresponding Jacobian matrix J are represented in block form as follows:

[0167]

[0168]

[0169] 5) P node and Lower bound reactive power deviation ΔQ of the node l The reactive power deviation ΔQ from the upper limit u There are a total of 2n² inequality constraints. The vector function h and the corresponding Jacobian matrix J, represented in blocks, are as follows:

[0170]

[0171]

[0172] 6) P node and Node lower bound voltage magnitude inequality constraint and upper limit voltage magnitude inequality constraint There are a total of 2n² vector functions, and the corresponding Jacobian matrix J is represented as follows:

[0173]

[0174]

[0175] 7) Lower bound active power deviation ΔP at node Vθ l Lower boundary reactive power deviation ΔQ l Upper boundary active power deviation ΔP u Upper limit reactive power deviation ΔQ u There are four in total. The vector function h and the corresponding Jacobian matrix J, represented in block form, are as follows:

[0176] h i5 =[ΔP l,n ΔP u,n ΔQ l,n ΔQ u,n ] T (25)

[0177]

[0178] The expressions for all elements are shown in formulas (28) and (29).

[0179]

[0180]

[0181] Having established the vector functions h and J0, we can obtain the vector functions F and J in the least squares problem by modifying them. The specific modifications are as follows:

[0182] F = h (29)

[0183] ee

[0184] F i =[h i ] + (30)

[0185] J e =J 0e (31)

[0186] (J i ) i =max{(h i ) i ,0}(J 0i ) i (32)

[0187] Thus, the vector function F and its corresponding Jacobian matrix J in the least squares problem are formed. The gradient of f is then:

[0188]

[0189] S4. The least squares problem obtained in step S3 is solved using the trust region method to obtain the adjustment amounts of variables such as generator output and node voltage in the power system, as well as the final power flow solution.

[0190] In another embodiment of the present invention, a power system power flow calculation system is provided. This system can be used to implement the above-mentioned power system power flow calculation method. Specifically, the power system power flow calculation system includes a construction module, a first conversion module, a second conversion module, and a calculation module.

[0191] Among them, the construction module establishes a new power constraint power flow model;

[0192] The first transformation module uses the method of constructing auxiliary functions to transform the inequalities in the obtained new power constraint power flow model into equal equations;

[0193] The second transformation module transforms the equations into bounded least squares problems;

[0194] The calculation module uses the trust region method to solve the least squares problem, obtaining the adjustment amounts of variables such as generator output and node voltage in the power system, as well as the final power flow solution.

[0195] In another embodiment of the present invention, a terminal device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to implement a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used for the operation of power system power flow calculation methods, including:

[0196] A novel power flow constrained model is established; the inequalities in the novel power flow constrained model are transformed into equations by constructing auxiliary functions; the equations are transformed into a bounded least squares problem; the trust region method is used to solve the least squares problem to obtain the adjustment amounts of variables such as generator output and node voltage in the power system, as well as the final power flow solution.

[0197] Please see Figure 6 The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When the processor 61 executes the computer program 63, it implements the power system power flow calculation method in this embodiment. To avoid repetition, these details are not elaborated here. Alternatively, when the processor 61 executes the computer program 63, it implements the functions of each model / unit in the power system power flow calculation system of this embodiment. To avoid repetition, these details are not elaborated here.

[0198] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 6 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0199] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0200] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or RAM of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0201] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0202] Please see Figure 7 The terminal device is a chip. In this embodiment, the chip 600 includes a processor 622, which may be one or more, and a memory 632 for storing computer programs executable by the processor 622. The computer program stored in the memory 632 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processor 622 may be configured to execute the computer program to perform the power system flow calculation method described above.

[0203] Additionally, chip 600 may also include a power supply component 626 and a communication component 650. The power supply component 626 can be configured to perform power management of chip 600, and the communication component 650 can be configured to enable communication of chip 600, such as wired or wireless communication. Furthermore, chip 600 may also include an input / output interface 658. Chip 600 can operate on an operating system stored in memory 632.

[0204] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor; these instructions can be one or more computer programs. It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device.

[0205] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the power system power flow calculation method in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps:

[0206] A novel power flow constrained model is established; the inequalities in the novel power flow constrained model are transformed into equations by constructing auxiliary functions; the equations are transformed into a bounded least squares problem; the trust region method is used to solve the least squares problem to obtain the adjustment amounts of variables such as generator output and node voltage in the power system, as well as the final power flow solution.

[0207] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0208] This invention utilizes Matlab as a platform to implement a constrained power flow model and algorithm system for obtaining novel power system operation modes. Calculations and analyses were performed on the IEEE 30-bus system and the IEEE 118-bus system. Data for both systems was obtained by reading case30 and case118 files from the MATPOWER package using Matlab. Different constrained power flow models were formed by relaxing different variables and setting different upper and lower bounds for the relaxation variables. The results were compared with those calculated using the Newton-Raphson method of MATPOWER. The results demonstrate the effectiveness of the constrained power flow model in expanding the solution space and investigate the model transformation mechanism for obtaining reasonable operation methods.

[0209] The embodiments for computational analysis in this invention are the IEEE 30-node system and the IEEE 118-node system. The IEEE 30-node and IEEE 118-node systems are commonly used standard test systems in the field of power systems, developed by the Institute of Electrical and Electronics Engineers (IEEE). They aim to provide a standardized platform for power system research, simulation, and testing. Both systems are built upon simplified power structure models, including key power system components such as generators, transformers, transmission lines, and loads. These components are interconnected by conductors, collectively forming the overall architecture of a power network.

[0210] The IEEE 30-node system has 6 generators and 41 branches, with a power base of 100 MVA; the IEEE 118-node system has 54 generators and 186 branches, with a power base of 100 MVA. Unless otherwise specified, the maximum number of iterations K is set by default. max =100, convergence accuracy ε=1×10 -5 .

[0211] Constrained power flow models are derived from traditional power flow models by relaxing some variables. Different constrained power flow models can be obtained by relaxing different numbers and types of variables. The solution space of power system power flow refers to the set of possible voltage magnitude and voltage phase angle solutions for a given system in power flow calculations.

[0212] When solving power flow problems in power systems, non-convergence may occur. Non-convergence is generally caused by the following two reasons:

[0213] 1) Ill-conditioned power flow problem: This refers to a problem where the power flow itself has a solution, but the algorithm is poor and it is difficult to find the solution.

[0214] 2) No solution for power flow: Due to improper load distribution and generator output configuration in the power system, the power system cannot obtain a reasonable real number solution when performing power flow calculations.

[0215] The constrained power flow model studied in this invention addresses the convergence problem of the Newton-Raphson algorithm in solving novel power systems. It aims to expand the solution space for ill-conditioned power flow problems encountered by the Newton-Raphson algorithm, making it plausible. When faced with an unsolvable power flow problem, the constrained power flow model can significantly relax the constraints on the output of individual generators, infinitely expanding the output range of relaxed generators—that is, infinitely relaxing the output of individual generators—thereby enabling the power flow calculation to converge. Subsequently, by observing the magnitude of the infinitely relaxed generator output, further analysis can be conducted to find effective measures for reasonably adjusting system parameters, such as adjusting the given output of other generators or reducing the load.

[0216] For the same system, convergence is easier when the load is smaller because simply reducing generator output is sufficient. However, as the load increases, the power flow becomes more ill-conditioned or even unsolvable because generator output is limited, making power balance difficult and thus hindering the finding of a suitable solution. This invention increases the system load to create an ill-conditioned power flow problem, observing whether different constrained power flow models have a solution space under the same load. This allows for analysis of the effectiveness of constrained power flow models in expanding the solution space. Under the same load, if constrained power flow model I converges but power flow model II diverges, it indicates that the solution space of power flow model I is larger than that of power flow model II. Similarly, for the same system, the effectiveness of constrained power flow models in expanding the solution space can be analyzed based on the maximum allowable load increase at convergence.

[0217] The active power output P and reactive power output Q of all relaxed generators are finitely relaxed, and the upper and lower bounds of the constraints are the corresponding upper and lower bounds of each generator in the actual system.

[0218] For the IEEE 30-bus system, the number of generator nodes corresponding to the relaxation of variables and the constraint rule d) are 1, 2, and 4, respectively, which form three constrained power flow models. By increasing the load of load nodes 3, 7, 15, and 30 and the total load, respectively, we observe whether there is a solution for different constrained power flow models and analyze the effectiveness of expanding the solution space of the constrained power flow models. The maximum allowable load increase when different constrained power flow models of the IEEE 30-bus system converge is shown in Table 1.

[0219] Table 1 Maximum load increase for different IEEE 30 models

[0220]

[0221] For the IEEE 118 system, the number of generator nodes corresponding to the relaxation of variables and constraint rule d) are 1, 14, and 24, respectively, forming three constrained power flow models. By increasing the load of load nodes 2, 52, and 101 and the total load, respectively, we observe whether different constrained power flow models have solutions and analyze the effectiveness of expanding the solution space of the constrained power flow models. The maximum allowable load increase when different constrained power flow models of the IEEE 118 node system converge is shown in the table below. It can be seen that the more relaxed generators there are, the greater the maximum allowable load increase when the model converges. Therefore, ill-conditioned problems that cannot be solved using models with fewer relaxed active generators under heavy loads can be solved well using models with more relaxed active generators. That is, increasing the number of relaxed active generators may increase the solution space of the power flow and solve the ill-conditioned problems that were originally unsolvable. Therefore, we can conclude that the more relaxed generators there are, the larger the solution space of the system's power flow. In traditional power flow calculations, only the generator output at node Vθ is infinitely relaxed, meaning the number of relaxed generators in a traditional power flow model is 1. However, in constrained power flow models, the number of relaxed generators can be reasonably and significantly increased, thus expanding the solution space of the power flow and effectively solving ill-conditioned power flows that traditional power flow models cannot address.

[0222] As the above analysis shows, increasing the number of slack variables may expand the solution space of the power flow. Furthermore, different constraints on the slack variables result in different sizes of the solution space. Clearly, the wider the upper and lower bounds of the slack variable constraints, the easier the power flow should converge, and the larger the solution space of the power flow.

[0223] Table 2 Maximum load increase for different IEEE 118 models

[0224]

[0225] Table 3 shows the convergence of IEEE 118 under different constraint models and conditions. As can be seen from Table 3, the more relaxed generators there are, the wider the upper and lower bounds of the constraints on the relaxed variables, the easier it is for the power flow to converge, and the larger the solution space of the power flow.

[0226] Table 3. Convergence results under different constraint models in IEEE 118

[0227]

[0228] Therefore, when the power flow does not converge, we can increase the solution space of the power flow calculation by increasing the number of slack variables and relaxing the constraints, thereby making the power flow converge.

[0229] As the above analysis shows, relaxing constraints or increasing slack variables can increase the convergence domain of power flow, making power flow calculations that were originally non-convergent converge. For non-convergent power flows, if the power flow itself has a solution (e.g., an ill-conditioned power flow), we can increase the number of slack variables, such as increasing the number of relaxed generators, and apply reasonable upper and lower bound constraints to the relaxed generators, thus making the power flow calculation converge to a feasible solution. However, before power flow calculation, we do not know whether the system has a solution under given parameters such as the current topology, generator output, and load level. If the power flow itself has no solution, relaxing variables and adding constraints to them may still not make the power flow converge. In this case, we can select some generator nodes for infinite relaxation. The advantage of this is that we can significantly expand the solution space of the power flow, potentially making a solution available for a system that was originally non-solvable. However, this solution may not be a feasible solution because in actual systems, generator output is limited. Infinitely relaxing the generator output may exceed its actual upper and lower bound constraints, which is unrealistic. Therefore, we need to adjust system parameters by infinitely relaxing the output of generator nodes to prevent them from exceeding limits, such as adjusting the given generator output, adjusting transformer taps, and adjusting reactive power compensation equipment. Generally, when the power flow constrained by upper and lower bounds has no solution, we first choose to infinitely relax the active power output of generator nodes. Then, based on the degree of active power output exceeding limits after the power flow converges, we adjust the output of nearby generators so that the active power output of infinitely relaxed generators returns to the actual upper and lower bounds when the power flow converges, thus bringing the power flow solution back to the feasible region and obtaining a reasonable operating mode. If the power flow solution still cannot return to the feasible region, we consider shedding loads to reduce the load level. Usually, we choose to infinitely relax the active power output P of generator nodes instead of the reactive power output Q of generator nodes because active power in a power system is easy to balance, but reactive power is not. Therefore, adjusting active power is often easier than adjusting reactive power.

[0230] This invention increases the load of load nodes to make the constrained power flow unsolvable, and then relaxes the active power output of generators infinitely to make the power flow converge. Then, based on the degree of the active power output of the infinitely relaxed generators exceeding the limit, the output of other generators is adjusted nearby to bring the power flow back into the feasible region, thus illustrating the model transformation mechanism for obtaining a reasonable operating mode.

[0231] For the IEEE30 system, the solution model applies infinite relaxation to generator 1 and finite relaxation to generator 25, allowing the required load power of node 3 to increase proportionally, i.e., setting the load power of node 3 to S. L3= k×(0.024+j0.012), when k=31, the power flow converges, but it is observed that the output of generator 1 is 0.82061+j0.32448, that is, the active power output exceeds the upper limit of 0.8. At this time, it is not a feasible solution, nor is it a feasible start-up method. At this time, it is only necessary to adjust the output of the generators near node 3. At the same time, it is observed that generator 22 has sufficient active power, so the active power output of generator 22 is increased, for example, let P Gset22 Increasing P from the original 0.2195 to 0.35 g22 =P Gset22 With other parts remaining unchanged, solving the model yields the generator output of node 1 as 0.67231 + j0.022464, returning to the feasible region.

[0232] For the IEEE 118 system, the solution model performs infinite relaxation on generator 1 and finite relaxation on generators 4, 6, and 69, allowing the load power of node 67 to increase proportionally, i.e., setting the load power of node 67 to S. L67 = k×(0.19+j0.02), when k=5, the power flow converges. At this time, the output of generator 1 is observed to be 1.1132+j0.15165, which means the active power output exceeds the upper bound of 1. This is not a feasible solution. At this time, it is necessary to adjust the output of generators near nodes 6 and 7. Therefore, the active power output of generator node 8 is increased, for example, let P g8 Increasing the value from 0 to 0.5 while keeping other parts unchanged, and solving the model, we can obtain the generator output of node 1 as 0.6395 + j0.15045, thus returning to the feasible region.

[0233] In traditional load flow (TLF) calculations using the Newton-Raphson algorithm, a single generator with a large capacity is designated as the balancing node to balance power, while the remaining generator nodes are PV nodes with given active power output and voltage amplitude. In contrast, in constrained load flow (CLF), a generator node with a given voltage amplitude is selected as the Vθ node. For other generator nodes, if both active power output and voltage amplitude are given, that node is designated as a PV node; if active power output is given but voltage amplitude is difficult to determine, the voltage amplitude of that generator is relaxed, and it is designated as a PV node. Node is Node P; if the generator output and voltage amplitude of this node are not easily determined, then this node is set as node PQVθ.

[0234] In power system power flow calculations, situations arise where the active power output and voltage amplitude of some generator nodes are difficult to determine. If the Newton-Raphson algorithm is used for power flow calculation in such cases, it is necessary to forcibly determine the active power output and voltage amplitude of these difficult-to-determine generator nodes to form PV nodes. This may lead to excessively high or low node voltage amplitudes in the power flow calculation results. Excessively high or low node voltage amplitudes can cause the following problems:

[0235] 1) Excessive voltage amplitude or voltage may cause equipment overload, difficulty in starting the equipment, affect the lifespan of the equipment, or even damage the equipment;

[0236] 2) Abnormal increases or decreases in voltage can reduce the stability of the power system. If the situation is serious, it may cause voltage collapse or even paralysis of the entire system, leading to large-scale power outages and equipment damage.

[0237] 3) Low voltage may also trigger relay protection, thereby changing the power grid topology and reducing transmission limits;

[0238] 4) Voltage that is too high or too low will reduce power quality, thereby reducing equipment efficiency and factory capacity.

[0239] For the IEEE 30 system, the traditional power flow solution using the Newton-Raphson method, given a voltage amplitude of 1 at the PV node and a given active power output, yields node voltage amplitudes within the range [0.9606, 1.0000], indicating good voltage quality and a feasible power flow solution. However, for renewable energy sources such as wind, solar, and solar power, due to their volatility, it is impossible to accurately determine their voltage amplitude and output. If the given voltage amplitude at the PV node is too low or too high, the voltage amplitude in the solution will be either too low or too high.

[0240] For example, in the IEEE 30 system, using the traditional power flow algorithm, if the voltage amplitude of the PV nodes is given as 0.98, it will be found that the voltage amplitude of many PQ nodes in the solution is lower than 0.95, the voltage quality is unqualified, and the solution is not feasible.

[0241] In the constrained power flow (CLF) model, we do not specify the voltage magnitude of the PV nodes, but instead give their upper and lower bounds as [0.95, 1.0]. 5], alsoEven without specifying the active power output, corresponding upper and lower bounds are given, meaning all PV nodes are relaxed to PQVθ nodes. To ensure the feasibility of the solution, the voltage amplitude of all PQ nodes is constrained to [0.95, 1.05]. If the output of the infinitely relaxed generator node exceeds the bounds after the solution, there are generally two solutions: the first is to adjust nearby generators according to the degree of bounds exceeded by the infinitely relaxed generator node; the second is to add the output of the infinitely relaxed generator node as a constraint to the original model.

[0242] The second solution is adopted here; solving the constrained power flow model yields a voltage amplitude range of [0.9671, 1.0148] for all nodes, and the output of each generator does not exceed the limit, which is a feasible solution and an efficient operating mode. Specific solution results are compared in Table 4.

[0243] Table 4. Calculation results under two IEEE 30 models

[0244]

[0245] For the IEEE 118 system, as shown in Table 5, similar conclusions hold. In the traditional Newton-Raphson algorithm, if the given voltage of the PV nodes is low, such as 0.98, the solved voltage amplitude is in the range [0.9399, 1.035]. Many PQ nodes have voltage amplitudes below 0.95, indicating poor power quality. However, after adopting the constrained power flow model, where we relax a portion of the generators (since the 118 system has 54 generators, without loss of generality, we relax 24 generators here), the solved voltage amplitudes are all in the range [0.9571, 1.0500], and the output of each relaxed generator does not exceed the limits, resulting in a feasible solution.

[0246] Table 5. Calculation results for two IEEE 118 models

[0247]

[0248] As the above analysis shows, constrained power flow requires fewer known quantities compared to traditional power flow. For values ​​that are difficult to define in traditional power flow, we only need to specify a range in constrained power flow. Based on the three node types in traditional power flow, six new node types have been added, allowing for flexible setting of known and unknown quantities. Furthermore, by applying appropriate constraints to slack variables, we can ensure that the solution process progresses towards the desired result, avoiding the unsatisfactory results after convergence in traditional power flow calculations. This enables a more efficient operation of the power system.

[0249] In new power systems, constrained power flow has good performance in solving ill-conditioned power flow and finding measures to adjust parameters when there is no solution for power flow. Constrained power flow can expand the solution space of power flow and solve problems that traditional power flow cannot solve.

[0250] However, constrained power flow also has its shortcomings compared to traditional power flow. In well-conditioned power flows where initial values ​​can be well-defined, the Newton-Raphson algorithm converges quickly, while constrained power flow requires slightly more iterations and computation time. The main reasons are twofold: First, constrained power flow introduces two one-sided inequality constraints when imposing upper and lower bounds on slack variables, or transforms one equation from one in traditional power flow into two one-sided inequalities. For example, imposing upper and lower bounds on the voltage magnitude of each PQ node in traditional power flow introduces 2^n1 one-sided inequalities, significantly increasing the number of equations and thus affecting computation speed and iteration count. Second, when initial values ​​are good (i.e., within the neighborhood of the power flow solution), Newton's method exhibits quadratic convergence, leading to rapid power flow convergence. However, the trust-region algorithm cannot guarantee that a Newton step is used in every step, thus increasing the number of iterations.

[0251] In summary, this invention provides a power system power flow calculation method and system. Addressing the difficulty of convergence of traditional power flow models and algorithms in the context of novel power systems, this invention relaxes and constrains some variables based on traditional power flow models to obtain a novel constrained power flow model for power systems, and solves this model using a trust-region algorithm. The main research and conclusions are as follows:

[0252] 1) A novel power flow constrained model was studied. This model breaks through the limitation of traditional power flow models that can only relax the output of one generator, thereby expanding the solution space of the power flow. Inequality constraints were added to the power flow model to reasonably constrain the control variables and state variables, ensuring that the power flow converges to a reasonable solution.

[0253] 2) A trust-region algorithm for efficiently solving inequalities and systems of equations was studied, and this algorithm was applied to solve a novel power system constrained power flow model. Example analysis demonstrates the effectiveness of the trust-region algorithm in solving the novel power system constrained power flow model.

[0254] 3) A power flow calculation program for power systems was developed and an example analysis was conducted. The results show that for benign power flows, the constrained power flow model can quickly converge to a reasonable solution; for ill-conditioned power flow problems faced by traditional power flow models, the constrained power flow model can expand the solution space of the power flow and find feasible solutions; for cases where there is no solution for the power flow, the constrained power flow model can significantly expand the solution space of the power flow by infinitely relaxing the output of some generators, thereby enabling the power flow to converge. Based on the degree of boundary crossing of infinitely relaxed generators and the network topology, parameter adjustment measures to bring the power flow back to the feasible region are given.

[0255] In new power systems, the ideas of constraint power flow variable relaxation and constraint proposed in this study can provide some theoretical guidance for solving ill-conditioned power flow and for parameter adjustment measures when there is no solution for power flow.

[0256] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0257] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0258] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0259] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0260] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0261] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0262] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random-access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0263] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1A device that provides the functions specified in one or more boxes.

[0264] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0265] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0266] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A power flow calculation method for a power system, characterized in that, Includes the following steps: Establish a new power flow constraint model; By constructing auxiliary functions, the inequalities in the obtained novel power flow constrained model are transformed into equations. Specifically, the transformation of the inequalities in the novel power flow constrained model into equations is as follows: The constrained power flow model is transformed into a system of nonlinear inequalities and nonlinear equations under standard bounded constraints, where the bilateral constraints of the upper and lower bounds are transformed into two unilateral constraints. Construct a penalty function to convert inequalities into equalities; The penalty function is constructed as follows: Based on the concept of penalty functions, an auxiliary function for continuously differentiable functions is constructed. By adding a penalty term related to the degree of constraint violation to the objective function, the value of the objective function increases when the constraint is violated. Transforming the equation into a bounded least squares problem specifically involves: Based on the construction of the auxiliary function, firstly, according to the input equation vector... And inequality vectors Forming the vector function h and its corresponding Jacobian matrix ; Then, based on the constructed auxiliary function, the vector function h and its corresponding Jacobian matrix are analyzed. After making corrections, we obtain F and its corresponding Jacobian matrix J; Transform the equation into a bounded least squares problem; The least squares problem is solved using the trust region method to obtain the adjustment amounts of generator output, node voltage variables, and the final power flow solution of the power system.

2. The power system power flow calculation method according to claim 1, characterized in that, In the new power flow constrained model, the equality constraint is expressed as: Inequality constraints in a constrained power flow model are expressed as: in, N Represents the set of all nodes. A This represents the set of nodes whose generator active power output has been relaxed. Table B This shows the set of nodes that have relaxed the reactive power output of the generator. C This represents the set of nodes whose node voltage magnitudes have been relaxed; for node i, Represents the real part of the voltage. Represents the real part of the current. Represents the imaginary part of voltage. Represents the imaginary part of the current. This represents the active power absorbed by the load. This indicates the active power output of the generator. This represents the reactive power absorbed by the load. This indicates the reactive power output of the generator. Indicates a given voltage amplitude. Indicates the lower bound of the iteration variable. Indicates the upper bound of the iteration variable. The real part of the nodal admittance matrix is ​​represented. This represents the imaginary part of the nodal admittance matrix.

3. The power system power flow calculation method according to claim 1, characterized in that, The least squares problem with bounded constraints is as follows: in, For iteration variables, The lower bound of the iteration variable, The upper bound of the iteration variable, This is the set of power flow equations after the inequalities are transformed into equations. The objective function is denoted as .

4. The power system power flow calculation method according to claim 1, characterized in that, For vector functions h and The block representation is as follows: in, Represents an equality vector. Represents an inequality vector; and for The partitioning, and They are respectively and The corresponding Jacobian matrix; to for The partitioning, to They are respectively to The corresponding Jacobian matrix; Active power deviation at PQ node reactive power deviation Equality constraints A vector function represented in blocks. and the corresponding Jacobian matrix Represented as: Active power deviation at node P Equality constraints A vector function represented in blocks. and the corresponding Jacobian matrix Represented as: Lower bound voltage magnitude inequality constraint at PQ node and upper limit voltage magnitude inequality constraint common A vector function represented in blocks. and the corresponding Jacobian matrix Represented as: Lower bound active power deviation of the node Deviation from upper limit of active power Inequality constraints A vector function represented in blocks. and the corresponding Jacobian matrix Represented as: P node and Lower bound reactive power deviation of the node Deviation from upper limit of reactive power Inequality constraints A vector function represented in blocks. and the corresponding Jacobian matrix Represented as: P node and Node lower bound voltage magnitude inequality constraint and upper limit voltage magnitude inequality constraint 2 in total A vector function represented in blocks. and the corresponding Jacobian matrix Represented as: Lower bound active power deviation of the node Lower boundary reactive power deviation Upper boundary active power deviation Upper limit reactive power deviation There are 4 in total, representing vector functions in blocks. and the corresponding Jacobian matrix Represented as: 。 5. The power system power flow calculation method according to claim 3, characterized in that, The objective function The gradient is: in, For the objective function f gradient, For the power flow equation vector F The corresponding Jacobian matrix transpose, The vector of the power flow equations after the inequalities are transformed into equations.

6. The power system power flow calculation method according to claim 5, characterized in that, For vector functions and its corresponding Jacobian matrix The specific corrections are as follows: in, This is the vector of the power flow equations after the inequalities are transformed into equations. is the vector of the power flow equation. This is the vector of the power flow inequality equations after the inequalities are transformed into equalities. Let be the vector of the power flow inequality equation. Let be the Jacobian matrix of the power flow equation vectors after the inequality is transformed into an equation. Let be the Jacobian matrix of the vectors in the power flow equation. is the Jacobian matrix of the power flow inequality equation vector after the inequality is transformed into an equality.

7. A power flow calculation system for a power system, characterized in that, include: Build modules to establish a new power constraint power flow model; The first transformation module, by constructing an auxiliary function, transforms the inequalities in the obtained new power constraint power flow model into equal equations. Specifically, the transformation of the inequalities in the new power constraint power flow model into equal equations is as follows: The constrained power flow model is transformed into a system of nonlinear inequalities and nonlinear equations under standard bounded constraints, where the bilateral constraints of the upper and lower bounds are transformed into two unilateral constraints. Construct a penalty function to convert inequalities into equalities; The penalty function is constructed as follows: Based on the concept of penalty functions, an auxiliary function for continuously differentiable functions is constructed. By adding a penalty term related to the degree of constraint violation to the objective function, the value of the objective function increases when the constraint is violated. Transforming the equation into a bounded least squares problem specifically involves: Based on the construction of the auxiliary function, firstly, according to the input equation vector... And inequality vectors Forming the vector function h and its corresponding Jacobian matrix ; Then, based on the constructed auxiliary function, the vector function h and its corresponding Jacobian matrix are analyzed. After making corrections, we obtain F and its corresponding Jacobian matrix J; The second transformation module transforms the equations into bounded least squares problems; The calculation module uses the trust region method to solve the least squares problem, obtaining the adjustment amounts of generator output and node voltage variables in the power system, as well as the final power flow solution.

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