Load flow calculation method, device and equipment based on polar coordinate form

Abstract

The embodiment of the invention provides a power flow calculation method, device and equipment based on a polar coordinate form, and relates to the technical field of electric power. The method comprises the following steps: constructing a polar coordinate system power flow equation based on power grid data read from a power grid system; performing full-pure embedding construction on the polar coordinate system power flow equation to obtain a full-pure embedding power flow model; inputting an auxiliary variable into the all-pure embedded power flow model to obtain a node voltage initial amplitude and a voltage initial phase; constructing a recursive equation by using the full-pure embedded power flow model and the auxiliary variables; solving the recursion equation step by step by using the node voltage initial amplitude and the voltage initial phase until the obtained power series voltage amplitude coefficient and the power series voltage phase coefficient are converged; and performing power series summation by using the power series voltage amplitude coefficient and the power series voltage phase coefficient to obtain a node voltage amplitude and a voltage phase. The convergence of load flow calculation can be remarkably improved.

Description

Technical Field

[0001] Embodiments of the present invention relate to the field of power technology. More specifically, embodiments of the present invention relate to a power flow calculation method, device, and equipment based on polar coordinate form. Background Art

[0002] Power flow calculation of a power system is a basic tool for power grid planning and operation analysis. Its core task is to obtain node voltages and phases by solving high-dimensional non-linear equations, providing key data support for system safety, stability, and economic dispatching.

[0003] Currently, the Newton-Raphson method (NR) widely used in the industry is based on the principle of iterative correction, and it is necessary to repeatedly generate the Jacobian matrix and solve the correction equation. However, with the increasing penetration rate of power electronic devices and the complexity of operation modes in a new type of power system, the limitations of the NR method are becoming increasingly prominent: First, the algorithm is sensitive to the selection of initial values, and unreasonable initial values may lead to slow convergence or even non-convergence; Second, in each iterative calculation, it is necessary to regenerate the Jacobian matrix and calculate the correction equation, resulting in a slow calculation speed of the NR method; Third, when the power flow does not converge, it is impossible to confirm whether the power flow itself has no solution or the power flow has a solution but the power flow solution has not been obtained.

[0004] In response to the above problems, the Holomorphic Embedding Method (HEM) power flow algorithm is proposed as a non-iterative algorithm. By embedding the power flow equation into the complex variable domain, constructing the variable to be solved as a holomorphic function, and recursively solving the coefficients based on the power series expansion, it does not require the selection of initial values and avoids the generation of the Jacobian matrix. When the power flow has a solution, it can ensure convergence, and when there is no solution, it clearly indicates through a numerical oscillation signal. In recent years, the HEM power flow algorithm has shown unique advantages in scenarios such as AC / DC hybrid systems, distributed energy clusters, and uncertainty analysis.

[0005] However, existing HEM power flow algorithms are all based on the rectangular coordinate system. Their power flow equations use the real and imaginary parts of the node voltage as variables, with many variables to be solved. The holomorphic embedding forms for different node types are constructed differently, and the derivation process is complex, thus affecting the efficiency and convergence of power flow calculation. Summary of the Invention

[0006] In this context, embodiments of the present invention are expected to provide a power flow calculation method, device, and equipment based on polar coordinate form and holomorphic embedding, which can improve the convergence of power flow calculation.

[0007] In the first aspect of the embodiments of the present invention, a power flow calculation method based on polar coordinate form is provided, including:

[0008] Construct a polar coordinate power flow equation based on the power grid data read from the power grid system;

[0009] Perform a holomorphic embedding construction on the polar coordinate power flow equation to obtain a holomorphic embedding power flow model;

[0010] Input the auxiliary variables into the holomorphic embedding power flow model to obtain the initial node voltage amplitude and the initial voltage phase;

[0011] Use the holomorphic embedding power flow model and the auxiliary variables to construct a recursive equation;

[0012] Use the initial node voltage amplitude and the initial voltage phase to solve the recursive equation step by step until the power series voltage amplitude coefficients and the power series voltage phase coefficients converge;

[0013] Use the power series voltage amplitude coefficients and the power series voltage phase coefficients to perform power series summation respectively to obtain the node voltage amplitude and the voltage phase.

[0014] In an embodiment of this implementation manner, the construction of the polar coordinate power flow equation based on the power grid data read from the power grid system includes:

[0015] Construct a node admittance matrix based on the power grid data read from the power grid system;

[0016] Construct an initial power flow equation based on the node admittance matrix; wherein, the initial power flow equation contains sine functions and cosine functions;

[0017] Perform Taylor expansion on the sine functions and the cosine functions in the initial power flow equation to obtain the polar coordinate power flow equation.

[0018] In an embodiment of this implementation manner, the polar coordinate power flow equation includes an active power equation and a reactive power equation. The construction of the holomorphic embedding power flow model by performing a holomorphic embedding construction on the polar coordinate power flow equation includes:

[0019] Perform a holomorphic embedding construction on the active power equation based on the embedding factor to obtain a holomorphic embedding active power equation; wherein, the holomorphic embedding active power equation includes a voltage phase embedding equation;

[0020] Perform a holomorphic embedding construction on the reactive power equation based on the embedding factor to obtain a holomorphic embedding reactive power equation; wherein, the holomorphic embedding reactive power equation includes the voltage phase embedding equation;

[0021] Construct a voltage amplitude embedding equation based on the embedding factor, the set value of the voltage amplitude of the PV node in the power grid data, and the set value of the voltage amplitude of the balancing node;

[0022] Combining the holomorphic-embedded active power equation, the holomorphic-embedded reactive power equation, and the voltage magnitude embedding equation yields the holomorphic-embedded power flow model.

[0023] In one embodiment of this implementation manner, inputting the auxiliary variables into the holomorphic-embedded power flow model to obtain the initial node voltage magnitude and the initial voltage phase includes:

[0024] Expanding the voltage magnitude embedding equation to obtain a voltage magnitude expansion function;

[0025] Expanding the voltage phase embedding equation to obtain a voltage phase expansion function;

[0026] Constructing auxiliary variables based on the voltage magnitude embedding equation;

[0027] Inputting the embedding factor with a value of 0, the voltage magnitude expansion function, the voltage phase expansion function, and the auxiliary variables into the holomorphic-embedded power flow model to obtain the initial node voltage magnitude and the initial voltage phase.

[0028] In one embodiment of this implementation manner, constructing a recursive equation using the holomorphic-embedded power flow model and the auxiliary variables includes:

[0029] Performing operations on the set values of the voltage magnitudes of PV nodes and the set value of the voltage magnitude of the slack node in the grid data based on the impulse function to obtain a power series voltage magnitude coefficient equation;

[0030] Constructing the active power equation based on the power series voltage magnitude coefficient equation, the previously obtained power series voltage phase coefficient equation, and the previously obtained power series auxiliary variable coefficient equation to obtain an active power recursive equation;

[0031] Constructing the reactive power equation based on the power series voltage magnitude coefficient equation, the power series voltage phase coefficient equation, and the power series auxiliary variable coefficient equation to obtain a reactive power recursive equation;

[0032] Combining the power series voltage magnitude coefficient equation, the active power recursive equation, and the reactive power recursive equation yields the recursive equation.

[0033] In one embodiment of this implementation manner, the specific construction method of the power series auxiliary variable coefficient equation is:

[0034] Constructing the power series auxiliary variable coefficient equation using the auxiliary variables, the initial node voltage magnitude, and the power series voltage magnitude coefficient equation.

[0035] In one embodiment of this implementation manner, solving the recursive equation order by order using the initial node voltage amplitude and the initial voltage phase until the power series voltage amplitude coefficients and the power series voltage phase coefficients obtained converge, includes:

[0036] Set the recursion count to 0;

[0037] Solve the recursive equation order by order using the recursion count, the initial node voltage amplitude, and the initial voltage phase to obtain the active power and the reactive power until the deviation value between the active power and the reactive power is less than a preset convergence deviation, then determine that the obtained power series voltage amplitude coefficients and the power series voltage phase coefficients converge;

[0038] Wherein, in each solving process, add the recursion count to the current solving count to obtain a new recursion count; and solve the recursive equation based on the new recursion count, the initial node voltage amplitude, and the initial voltage phase to obtain the power series voltage amplitude coefficients and the power series voltage phase coefficients; and solve the power series auxiliary variable coefficient equation based on the new recursion count and the power series voltage amplitude coefficients to obtain the current power series auxiliary variable coefficients; and calculate the active power and the reactive power using the polar coordinate power flow equation for the power series voltage amplitude coefficients, the power series voltage phase coefficients, and the current power series auxiliary variable coefficients.

[0039] In one embodiment of this implementation manner, the active power equation of the polar coordinate power flow equation is:

[0040]

[0041] Wherein, P i is the active power injected into node i in the grid data; U i represents the node voltage amplitude of node i in the grid data, U j represents the node voltage amplitude of node j in the grid data, N is the number of nodes in the grid data; G ij is the conductance part of the node admittance matrix; δ ij is the voltage phase difference between node i and node j;

[0042] And, the reactive power equation of the polar coordinate power flow equation is:

[0043]

[0044] Wherein, Q i is the reactive power injected into node i in the grid data; B ij is the susceptance part of the node admittance matrix.

[0045] In the second aspect of the embodiments of the present invention, a power flow calculation device based on polar coordinate form is provided, including:

[0046] A first construction unit, configured to construct a polar coordinate system power flow equation based on power grid data read from a power grid system;

[0047] A second construction unit, configured to perform a holomorphic embedding construction on the polar coordinate system power flow equation to obtain a holomorphic embedding power flow model;

[0048] An input unit, configured to input an auxiliary variable into the holomorphic embedding power flow model to obtain an initial node voltage amplitude and an initial voltage phase;

[0049] A third construction unit, configured to construct a recurrence equation by using the holomorphic embedding power flow model and the auxiliary variable;

[0050] A solving unit, configured to sequentially solve the recurrence equation by using the initial node voltage amplitude and the initial voltage phase until the power series voltage amplitude coefficients and the power series voltage phase coefficients obtained converge;

[0051] A summing unit, configured to perform power series summation by using the power series voltage amplitude coefficients and the power series voltage phase coefficients respectively to obtain a node voltage amplitude and a voltage phase.

[0052] In the third aspect of the embodiments of the present invention, a computing device is provided, where the computing device includes: at least one processor, a memory, and an input / output unit; wherein, the memory is used to store a computer program, and the processor is used to call the computer program stored in the memory to execute the method according to any one of the first aspect.

[0053] In the fourth aspect of the embodiments of the present invention, a computer-readable storage medium is provided, which includes instructions that, when running on a computer, cause the computer to execute the method according to any one of the first aspect.

[0054] In the fifth aspect of the embodiments of the present invention, a computer program product is provided, including a computer program that, when executed by a processor, implements the method according to any one of the first aspect.

[0055] The power flow calculation method, device and equipment based on the polar coordinate form according to the embodiments of the present invention can construct a power flow equation in the polar coordinate system based on the power grid data read from the power grid system, reduce the number of solution variables, and lower the computational complexity; adopt the holomorphic embedding to construct the model, avoid relying on the initial value selection and complex iteration process, simplify the calculation process, and improve the stability and reliability; use the auxiliary variable to obtain the initial value to solve the recurrence equation, and ensure convergence to the correct result. These characteristics enable the steps of the calculation process to be closely connected, the calculation logic to be simple and efficient, reduce unnecessary computational overhead, and ultimately significantly improve the convergence of the power flow calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] By reading the following detailed description with reference to the accompanying drawings, the above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily understood. In the drawings, several embodiments of the present invention are shown by way of illustration and not limitation, wherein:

[0057] Figure 1 It is a schematic flow chart of the power flow calculation method based on the polar coordinate form provided by an embodiment of the present invention;

[0058] Figure 2 It is a schematic diagram of the convergence curve of the node power system provided by an embodiment of the present invention;

[0059] Figure 3 It is a schematic diagram of the comparison of the convergence of the power flow calculation method in polar coordinate form and the classical power flow calculation method provided by an embodiment of the present invention;

[0060] Figure 4 It is a schematic flow chart of the power flow calculation method based on the polar coordinate form provided by another embodiment of the present invention;

[0061] Figure 5 It is a schematic structural diagram of the power flow calculation device based on the polar coordinate form provided by an embodiment of the present invention;

[0062] Figure 6 It schematically shows a structural diagram of a medium according to an embodiment of the present invention;

[0063] Figure 7 It schematically shows a structural diagram of a computing device according to an embodiment of the present invention.

[0064] In the drawings, the same or corresponding reference numerals indicate the same or corresponding parts. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0065] The principles and spirit of the present invention will be described below with reference to several exemplary embodiments. It should be understood that these embodiments are provided only to enable those skilled in the art to better understand and then implement the present invention, rather than to limit the scope of the present invention in any way. On the contrary, these embodiments are provided to make the present disclosure more thorough and complete, and to be able to fully convey the scope of the present disclosure to those skilled in the art.

[0066] Those skilled in the art know that the embodiments of the present invention can be implemented as a system, a device, equipment, a method, or a computer program product. Therefore, the present disclosure can be specifically implemented in the following forms, namely: completely hardware, completely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software.

[0067] According to an embodiment of the present invention, a power flow calculation method, device, and equipment based on polar coordinate form are proposed.

[0068] It should be noted that the quantity of any element in the drawings is for illustration rather than limitation, and any naming is only for distinction and does not have any limiting meaning.

[0069] The principles and spirit of the present invention will be explained in detail below with reference to several representative embodiments of the present invention.

[0070] Exemplary method

[0071] The following reference Figure 1 , Figure 1 is a schematic flowchart of a power flow calculation method based on polar coordinate form provided for an embodiment of the present invention. It should be noted that the embodiments of the present invention can be applied to any applicable scenario.

[0072] Figure 1 The flow of a power flow calculation method based on polar coordinate form provided for an embodiment of the present invention shown in the figure includes:

[0073] Step S101, constructing a polar coordinate system power flow equation based on the power grid data read from the power grid system.

[0074] In the embodiments of the present invention, the polar coordinate power flow equations (PCPFE) refer to a mathematical model for power flow calculation established based on the node power balance relationship after expressing the node voltages of the power system in polar coordinate form of amplitude and phase angle. The polar coordinate power flow equations include active power equations and reactive power equations. Power flow calculation (PFC) refers to a numerical calculation process of solving the voltage amplitudes and phase angles of each node in the entire system, as well as the line power flow and power distribution, based on the known partial node voltages and load conditions of the power system. This calculation is based on the steady-state operation model of the power system and is one of the basic tools for power grid planning, dispatching, and analysis.

[0075] In the embodiments of the present invention, the power grid data may include information such as loads and line parameters.

[0076] As an optional implementation manner, the method of constructing the polar coordinate power flow equations based on the power grid data read from the power grid system in step S101 may include:

[0077] Construct a node admittance matrix based on the power grid data read from the power grid system;

[0078] Construct an initial power flow equation based on the node admittance matrix; wherein, the initial power flow equation contains sine functions and cosine functions;

[0079] Perform Taylor expansion on the sine functions and cosine functions in the initial power flow equation to obtain the polar coordinate power flow equations.

[0080] Among them, by implementing this implementation manner, through Taylor series expansion of the sine functions and cosine functions in the initial power flow equation, the non-linear trigonometric function terms are transformed into polynomial forms, effectively eliminating the complex non-linear interference caused by phase angle differences in the polar coordinate equations, and significantly simplifying the construction process of the holomorphic embedding model; at the same time, the polynomial structure after Taylor expansion is easier to solve recursively, reducing the computational complexity of the high-order power series coefficients. Combining with the physical characteristics of the node admittance matrix, on the premise of ensuring the accuracy of the power flow equations, the recursive iteration efficiency is greatly improved, providing a mathematical basis for the rapid power flow calculation of large-scale power grids, and reducing the consumption of computing resources at the same time.

[0081] In the embodiments of the present invention, Taylor expansion (TE) refers to a mathematical method of approximating a function in the form of a power series based on the derivative information at a certain point of the function.

[0082] In the embodiments of the present application, the initial power flow equation may be:

[0083]

[0084] Among them, P i is the active power injected into node i in the grid data; Q i is the reactive power injected into node i in the grid data; B ij is the susceptance part of the node admittance matrix, U i represents the node voltage amplitude of node i in the grid data, U j represents the node voltage amplitude of node j in the grid data, N is the number of nodes in the grid data; G ij is the conductance part of the node admittance matrix; δ ij is the voltage phase difference between node i and node j.

[0085] For the convenience of constructing the subsequent holomorphic embedding form, the initial power flow equation is sorted out to obtain Equation (2):

[0086]

[0087] Based on the above analysis, the key design of this paper is to eliminate the trigonometric functions in the equation and use Taylor expansion for processing. Equation (3) gives the expansion forms of the sine and cosine functions.

[0088]

[0089] Substituting Equation (3) into Equation (2), the polar coordinate power flow equation (4) without trigonometric functions can be obtained:

[0090]

[0091] Among them, the first equation in Equation (4) is the active power equation, and the second equation is the reactive power equation.

[0092] Theoretically speaking, Equation (4) is not exactly the same as Equation (2), but since the phase angle difference between the two ends of the line is usually small, it is feasible to use Equation (4) to replace Equation (2) under certain accuracy requirements.

[0093] In the embodiment of this application, the node admittance matrix is shown in Equation (5):

[0094]

[0095] Among them, is the series part of the conductance matrix, is the parallel part of the conductance matrix; is the series part of the susceptance matrix, and are the series part and the parallel part of the admittance matrix respectively.

[0096] In step S102, a holomorphic embedding construction is performed on the polar coordinate power flow equation to obtain a holomorphic embedding power flow model.

[0097] In the embodiment of the present application, the Holomorphic Embedding Method (HEM) is a non-iterative algorithm for power flow calculation in power systems.

[0098] As an alternative implementation, the method of performing a holomorphic embedding construction on the polar coordinate power flow equation in step S102 to obtain a holomorphic embedding power flow model may include:

[0099] Perform a holomorphic embedding construction on the active power equation based on the embedding factor to obtain a holomorphic embedding active power equation; wherein, the holomorphic embedding active power equation includes a voltage phase embedding equation;

[0100] Perform a holomorphic embedding construction on the reactive power equation based on the embedding factor to obtain a holomorphic embedding reactive power equation; wherein, the holomorphic embedding reactive power equation includes a voltage phase embedding equation;

[0101] Based on the embedding factor, the voltage magnitude setting value of the PV node in the grid data, and the voltage magnitude setting value of the slack node, construct a voltage magnitude embedding equation;

[0102] Combine the holomorphic embedding active power equation, the holomorphic embedding reactive power equation, and the voltage magnitude embedding equation to obtain a holomorphic embedding power flow model.

[0103] Among them, in this implementation, by introducing an embedding factor, a systematic holomorphic embedding of the active power equation, reactive power equation, and voltage magnitude constraint in the polar coordinate system is performed to construct a structurally unified holomorphic embedding power flow model. This method innovatively embeds the voltage phase and magnitude into the complex variable domain respectively. By separating the embedding processes of the active / reactive power equations and the voltage magnitude constraint, it not only retains the physical intuitiveness of the polar coordinate form but also realizes a decoupled recursive solution mechanism for each variable. In particular, the independent embedding of the voltage magnitude setting values of the PV node and the slack node ensures strict constraints on key operating parameters and effectively solves the problem of inaccurate voltage control in traditional methods under heavy load scenarios. This modular embedding method not only simplifies the derivation process of high-order power series coefficients but also significantly improves the calculation efficiency through a unified holomorphic embedding framework, providing a reliable guarantee for the fast convergence and high-precision solution of the power flow in complex power systems.

[0104] In the embodiment of the present invention, the holomorphic embedding active power equation can be as shown in Equation (6):

[0105]

[0106] Wherein, α represents the embedding factor, and for the voltage magnitude embedding equation is U i(α); The voltage phase embedding equation is in the form of δ ij (α) = δ i (α) - δ j (α).

[0107] In the embodiment of the present invention, the holomorphic embedding reactive power equation can be as shown in Equation (7):

[0108]

[0109] Wherein, is the shunt susceptance of node i.

[0110] In the embodiment of the present invention, the voltage magnitude embedding equation is as shown in Equation (8):

[0111]

[0112] Wherein, Ω PQ is the set of PQ nodes; is the set value of the voltage magnitude of node i. The voltage magnitudes of PV nodes and slack nodes are given.

[0113] Step S103: Input the auxiliary variables into the holomorphic embedding power flow model to obtain the initial voltage magnitude and initial voltage phase of the nodes.

[0114] As an alternative implementation, the manner of inputting the auxiliary variables into the holomorphic embedding power flow model in step S103 to obtain the initial voltage magnitude and initial voltage phase of the nodes may include:

[0115] Expand the voltage magnitude embedding equation to obtain a voltage magnitude expansion function;

[0116] Expand the voltage phase embedding equation to obtain a voltage phase expansion function;

[0117] Construct auxiliary variables based on the voltage magnitude embedding equation;

[0118] Input the embedding factor with a value of 0, the voltage magnitude expansion function, the voltage phase expansion function, and the auxiliary variables into the holomorphic embedding power flow model to obtain the initial voltage magnitude and initial voltage phase of the nodes.

[0119] Among them, by implementing this implementation, a systematic initial solution acquisition mechanism is constructed by expanding the voltage magnitude and phase embedding functions and introducing auxiliary variables to handle the non-linear terms. By setting the embedding factor to zero, the initial state solution process of the holomorphic embedding power flow model is directly simplified, enabling the initial voltage magnitude and phase of the nodes to be quickly determined through linearized equations. This method not only avoids the sensitivity dependence of the traditional iterative method on the initial value but also effectively solves the non-linear problem of the voltage reciprocal term in polar coordinates through the introduction of auxiliary variables, significantly improving the accuracy and stability of the initial solution.

[0120] In the embodiment of the present invention, the voltage amplitude embedding equation U i (α) The voltage amplitude expansion function and the voltage phase embedding equation δ obtained by expansion i (α) The voltage phase expansion function obtained by expansion can be as shown in Equation (9):

[0121]

[0122] Since there are reciprocal terms of voltage on the right sides of Equations (6) and (7), and the power series coefficients of the voltage are unknown, a new auxiliary variable W i (α) is introduced, as shown in Equation (10):

[0123]

[0124] Based on Equation (10), it is derived that the recursive relation expression of the power series coefficients of W i [n] (i.e., the power series auxiliary variable coefficient equation) is as shown in Equation (11):

[0125]

[0126] Among them, U i [n] is the power series voltage amplitude coefficient equation, W i [0] is the auxiliary variable, and U i [0] is the initial amplitude of the node voltage.

[0127] In the embodiment of the present invention, substituting Equations (9)-(10) into (6)(7)(8) and setting the embedding variable α to 0, Equations (12)-(14) can be obtained:

[0128]

[0129] Among them, δ ij [0] = δ i [0] - δ j [0]. It is not difficult to infer that by setting the initial voltage phase δ i [0] = 0 for all nodes and the initial amplitude U of the node voltage i [0] = 1, Equations (12)-(14) can be satisfied. This value is also the initial solution to be sought.

[0130] Step S104: Use the holomorphic embedding power flow model and the auxiliary variable to construct a recursive equation.

[0131] As an alternative implementation manner, the method for using the holomorphic embedding power flow model and the auxiliary variable in Step S104 to construct a recursive equation may include:

[0132] Based on the impulse function, the voltage amplitude set values of PV nodes and the voltage amplitude set values of balance nodes in the power grid data are calculated to obtain the power series voltage amplitude coefficient equation;

[0133] Based on the power series voltage amplitude coefficient equation, the power series voltage phase coefficient equation obtained in advance, and the power series auxiliary variable coefficient equation obtained in advance, the active power equation is constructed to obtain the active power recursive equation;

[0134] Based on the power series voltage amplitude coefficient equation, the power series voltage phase coefficient equation, and the power series auxiliary variable coefficient equation, the reactive power equation is constructed to obtain the reactive power recursive equation;

[0135] The power series voltage amplitude coefficient equation, the active power recursive equation, and the reactive power recursive equation are combined to obtain the recursive equation.

[0136] Among them, in this implementation method, by introducing the impulse function to process the voltage amplitude constraints of PV nodes and balance nodes, a structured recursive equation system is constructed. This method innovatively unifies and integrates the voltage amplitude coefficient equation, the phase coefficient equation, and the auxiliary variable coefficient equation, realizing the collaborative recursive solution of the active power equation and the reactive power equation. Through the precise mathematical representation of the impulse function, the strict constraint of the PV node voltage amplitude is ensured, effectively solving the problem of voltage instability of traditional methods under extreme working conditions. This modular recursive equation construction method not only simplifies the derivation process of high-order power series coefficients but also significantly reduces the calculation dimension through variable decoupling, making each order of recursion only require solving a linear equation system, greatly improving the calculation efficiency.

[0137] In the embodiment of the present invention, similarly, substituting equations (9)-(10) into (6)(7)(8), and making the nth-order power series coefficients of the factor α on both sides of the equation equal, the recursive equation can be obtained. Specifically, the corresponding equations of the active power recursive equation and the reactive power recursive equation are shown in (15) and (16); the corresponding equations of the power series voltage amplitude coefficient equations of the balance node and the PV node are shown in (17).

[0138]

[0139]

[0140]

[0141] where δ ij [n], has the following meanings as shown in (18)-(20); μ n1 is the impulse function, and its value is as shown in (21):

[0142] δ ij [n] = δi [n] - δ j [n](18)

[0143]

[0144] Unify the relationships of the recursive equations shown in (15)-(18), so that all the coefficients of the nth-order power series are on the left side of the equation, and all the coefficients of the power series lower than the nth order are on the right side of the equation. The constructed unified recursive equation can be expressed as Equation (22):

[0145] A·x[n] = b[n - 1] (22)

[0146] Among them, A is the recursive matrix required for recursive calculation and remains constant during the recursive calculation process; x[n] is the coefficient of the nth-order power series to be solved; b[n - 1] is the right-side term of the recursive equation, and this term is calculated from the coefficients of the power series lower than the nth order.

[0147] Optionally, the construction method of the power series auxiliary variable coefficient equation is specifically:

[0148] Construct the power series auxiliary variable coefficient equation using auxiliary variables, the initial amplitude of the node voltage, and the power series voltage amplitude coefficient equation.

[0149] Step S105, use the initial amplitude of the node voltage and the initial voltage phase to solve the recursive equation order by order until the obtained power series voltage amplitude coefficient and power series voltage phase coefficient converge.

[0150] As an optional implementation manner, the way of using the initial amplitude of the node voltage and the initial voltage phase to solve the recursive equation order by order in step S105 until the obtained power series voltage amplitude coefficient and power series voltage phase coefficient converge may include:

[0151] Set the number of recursive times to 0;

[0152] Use the number of recursive times, the initial amplitude of the node voltage, and the initial voltage phase to solve the recursive equation order by order to obtain the active power and reactive power until the deviation value of the active power and reactive power is less than the preset convergence deviation, then it is determined that the obtained power series voltage amplitude coefficient and power series voltage phase coefficient converge;

[0153] Wherein, in each solution process, the recursion count is added to the current solution count to obtain a new recursion count; and based on the new recursion count, the initial node voltage amplitude, and the initial voltage phase, the recursive equation is solved to obtain the power series voltage amplitude coefficients and the power series voltage phase coefficients; and based on the new recursion count and the power series voltage amplitude coefficients, the power series auxiliary variable coefficient equation is solved to obtain the current power series auxiliary variable coefficients; and the polar coordinate power flow equation is used to calculate the power series voltage amplitude coefficients, the power series voltage phase coefficients, and the current power series auxiliary variable coefficients to obtain the active power and the reactive power.

[0154] Wherein, by implementing this implementation manner, through setting the recursion count and adopting a step-by-step solution mechanism, the efficient convergence of the holomorphic embedding power flow model is achieved. This method innovatively uses the initial voltage amplitude and phase as the recursion starting point, and by dynamically updating the recursion count and solving the coefficients of each order in a loop, the systematicness and stability of the calculation process are ensured. Using the preset convergence deviation as the iteration termination condition not only ensures the calculation accuracy but also avoids the convergence failure problem that may occur in the traditional iterative method. In each recursion process, this method synchronously updates the voltage amplitude coefficients, the phase coefficients, and the auxiliary variable coefficients, and checks the power deviation in real time through the polar coordinate power flow equation, forming a closed-loop feedback mechanism.

[0155] Step S106, use the power series voltage amplitude coefficients and the power series voltage phase coefficients to perform power series summation respectively to obtain the node voltage amplitude and the voltage phase.

[0156] For example, the proposed polar coordinate HEM is analyzed and verified through multiple test cases, including the 3-node system, case39, case57, case118, case1354pegase, case2383wp, and case3120sp systems. The power flow calculation results are compared with the classical HEM method and the iterative NR method. All simulation case data are from MATPOWER. The algorithm proposed in the present invention uses the PyCharm software platform (Python version 3.11.7). Based on this platform, the proposed polar coordinate HEM algorithm and the classical HEM algorithm are developed and compared with the NR power flow calculation results in the open-source software PYPOWER. The maximum recursion count of the polar coordinate HEM and the classical HEM proposed in this paper is set to 30 times. The hardware platform uses a personal laptop with an Intel Core i9 CPU (5.2GHz) and 32GB of memory.

[0157] Please refer to Figure 2 , Figure 2Schematic diagram of the convergence curve of the node power system provided by an embodiment of the present invention; and the power flow results of the power flow calculation method based on the polar coordinate form (i.e., marked as "proposed polar coordinate HEM" in the figure) provided by the embodiment of the present invention are compared with the results of the NR method. From Figure 2 It can be seen that in this system, only 7 recursive calculations are required to achieve a convergence result of 10-6; and the proposed algorithm converges to the same voltage value as the NR method.

[0158] To verify the accuracy of the power flow calculation method based on the polar coordinate form, the present invention conducts tests on multiple standard examples, and compares the calculation results with the power flow results of the NR method, with the NR method as the benchmark. The errors of four electrical quantities, namely voltage magnitude, voltage phase angle, active power, and reactive power, are compared, and the results are shown in Table 1. The convergence accuracy is set to 10-6 p.u. Among them, p.u. represents per unit, which is a commonly used numerical marking method in power system and engineering calculations, representing the relative values of various physical quantities and parameters, and is dimensionless.

[0159] As can be seen from Table 1, in multiple systems, the maximum error of the voltage magnitude is at the 10-6 p.u. level, and the error of the phase angle is about at the 10-4° level. This shows that the proposed algorithm can converge to the same result as the NR method in these examples, verifying the accuracy of the proposed algorithm.

[0160] Table 1 Verification of the accuracy of the algorithm on multiple systems

[0161] Electrical quantity case118 case1354pegase case2383wp case3120sp |U| (p.u) <![CDATA[2.76×10 -8 > <![CDATA[1.88×10 -6 > <![CDATA[4.04×10 -7 > <![CDATA[1.52×10 -7 > δ (°) <![CDATA[8.52×10 -6 > <![CDATA[1.96×10 -4 > <![CDATA[1.86×10 -5 > <![CDATA[7.89×10 -6 > P (p.u) <![CDATA[3.00×10 -7 > <![CDATA[9.28×10 -5 > <![CDATA[3.56×10 -6 > <![CDATA[1.46×10 -5 > Q (p.u) <![CDATA[9.09×10 -7 > <![CDATA[2.70×10 -5 > <![CDATA[2.83×10 -5 > <![CDATA[1.22×10 -5 >

[0162] Please refer to Figure 3 , Figure 3 Schematic diagram of the comparison of the convergence of the power flow calculation method in polar coordinate form and the classical power flow calculation method provided by an embodiment of the present invention; shows the convergence curves of the classical power flow calculation method (i.e., marked as "classical HEM" in the figure) and the power flow calculation method in polar coordinate form (i.e., marked as "proposed polar coordinate HEM") in the 57-node, 118-node, and 300-node systems, and draws a convergence curve graph of the maximum power error varying with the number of recursive calculations. It can be seen that both the power flow calculation method in polar coordinate form and the classical power flow calculation method can converge after a finite number of recursive calculations.

[0163] This method first performs a Taylor expansion on the trigonometric functions in the polar coordinate power flow equation, then constructs an embedded form for the active power equation and reactive power equation of the power flow. The constructed holomorphic embedded form ensures that the initial solution is easy to obtain, and a recursive equation for high-order power series calculation is derived, inventing a reliable power flow calculation method based on polar coordinate holomorphic embedding.

[0164] It is also proposed that the solution of the non - linear equation system is non - iterative, has low dependence on the initial value, can ensure convergence when there is a solution, and can send a signal when oscillation occurs in the case of no solution.

[0165] The embedded form proposed in the present invention only needs to construct the active power equation and the reactive power equation, without distinguishing between PQ and PV nodes, and without introducing a new PV - node reactive power injection variable, and the derivation process is simpler.

[0166] In addition, the present invention can maintain the voltage amplitude of the PV node at a set value under power system operating conditions such as extreme overload.

[0167] Compared with the prior art, this method has higher reliability, lower dependence on the selection of the initial value, and can send a signal when the equation has no solution; the derivation process of the present invention only needs to be aimed at the active power equation and the reactive power equation, without introducing a new PV - node injected reactive power variable, and the derivation process is relatively simple; in addition, the dimension of the left - hand matrix of the recursive equation proposed is lower.

[0168] Please refer to Figure 4 , Figure 4 which is a schematic flow chart of the power flow calculation method based on the polar coordinate form provided by another embodiment of the present invention; as can be seen from Figure 4 , the power flow calculation method based on the polar coordinate form provided by another embodiment can perform the following steps:

[0169] 1. Read the data of the power grid; the data of the power grid includes information such as loads and line parameters;

[0170] 2. Construct the polar - coordinate power flow calculation equation through the Taylor expansion of trigonometric functions, and construct the corresponding holomorphic embedding model;

[0171] 3. Obtain the initial values of the node voltage amplitude and phase angle \(U i [0]=1\) and \(\delta i [0]=0\);

[0172] 4. Set the recursion count \(n = 1\);

[0173] 5. Obtain the higher - order power - series coefficients \(U i [n]\) and \(\delta i [n]\) by solving the recursive equation;

[0174] 6. Solve \(W i [n]\);

[0175] 7. Obtain the voltage amplitude \(U i [n]\) and \(\delta i [n]\) based on the obtained power series \(U i \) and voltage phase \(\delta i \);

[0176] 8. Determine convergence according to the power equation?

[0177] 9. If the power equation does not converge, then n = n + 1, and execute steps 5 - 8;

[0178] 10. If the power equation converges, then output the voltage magnitude U i and voltage phase δ i .

[0179] The present invention can make each step of the calculation process closely connected, the calculation logic simple and efficient, reduce unnecessary calculation overhead, and ultimately significantly improve the efficiency of power flow calculation. In addition, the present invention can also greatly improve the recursive iteration efficiency on the premise of ensuring the accuracy of the power flow equation, provide a mathematical basis for the rapid power flow calculation of large-scale power grids, and at the same time reduce the consumption of computing resources. In addition, the present invention can also simplify the derivation process of high-order power series coefficients, and significantly improve the calculation efficiency through a unified holomorphic embedding framework, providing a reliable guarantee for the rapid convergence and high-precision solution of power flows in complex power systems. In addition, the present invention can also avoid the sensitivity dependence on the initial value of the traditional iterative method, and effectively solve the non-linear problem of the voltage reciprocal term in polar coordinate form by introducing auxiliary variables, significantly improving the accuracy and stability of the initial solution. In addition, the present invention can also ensure the calculation accuracy and avoid the convergence failure problem that may occur in the traditional iterative method.

[0180] Exemplary device

[0181] After introducing the method of the exemplary embodiment of the present invention, next, with reference to Figure 5 an exemplary embodiment of the present invention will be described for a power flow calculation device based on polar coordinate form. The device includes:

[0182] A first construction unit 501, configured to construct a polar coordinate system power flow equation based on power grid data read from a power grid system; the polar coordinate system power flow equation includes an active power equation and a reactive power equation;

[0183] In the embodiment of the present invention, the active power equation of the polar coordinate system power flow equation is:

[0184]

[0185] where P i is the active power injected by node i in the power grid data; U i represents the node voltage magnitude of node i in the power grid data, U j represents the node voltage magnitude of node j in the power grid data, N is the number of nodes in the power grid data; G ij is the conductance part of the node admittance matrix; δ ijis the voltage phase difference between the node i and the node j;

[0186] Moreover, the reactive power equation of the polar coordinate power flow equation is:

[0187]

[0188] where Q i is the reactive power injected into the node i in the power grid data; B ij is the susceptance part of the node admittance matrix.

[0189] The second construction unit 502 is configured to perform a holomorphic embedding construction on the polar coordinate power flow equation to obtain a holomorphic embedding power flow model;

[0190] The input unit 503 is configured to input auxiliary variables into the holomorphic embedding power flow model to obtain the initial node voltage amplitude and the initial voltage phase;

[0191] The third construction unit 504 is configured to construct a recurrence equation by using the holomorphic embedding power flow model and the auxiliary variables;

[0192] The solving unit 505 is configured to solve the recurrence equation order by order by using the initial node voltage amplitude and the initial voltage phase until the power series voltage amplitude coefficients and the power series voltage phase coefficients obtained converge;

[0193] The summation unit 506 is configured to perform power series summation by using the power series voltage amplitude coefficients and the power series voltage phase coefficients respectively to obtain the node voltage amplitude and the voltage phase.

[0194] As an optional implementation manner, the specific manner in which the first construction unit 501 constructs the polar coordinate power flow equation based on the power grid data read from the power grid system may be:

[0195] Construct a node admittance matrix based on the power grid data read from the power grid system;

[0196] Construct an initial power flow equation based on the node admittance matrix; wherein, the initial power flow equation includes sine functions and cosine functions;

[0197] Perform Taylor expansion on the sine functions and cosine functions in the initial power flow equation to obtain the polar coordinate power flow equation.

[0198] Among them, when implementing this implementation method, by performing Taylor series expansion on the sine and cosine functions in the initial power flow equation, the non-linear trigonometric function terms are transformed into polynomial forms, effectively eliminating the complex non-linear interference caused by the phase angle difference in the polar coordinate equation, and significantly simplifying the construction process of the holomorphic embedding model. At the same time, the polynomial structure after Taylor expansion is easier to solve recursively, reducing the computational complexity of the high-order power series coefficients. Combining with the physical characteristics of the nodal admittance matrix, on the premise of ensuring the accuracy of the power flow equation, the recursive iteration efficiency is greatly improved, providing a mathematical basis for the rapid power flow calculation of large-scale power grids and reducing the consumption of computing resources.

[0199] As an optional implementation method, the specific way for the second construction unit 502 to perform holomorphic embedding construction on the polar coordinate system power flow equation to obtain the holomorphic embedding power flow model can be as follows:

[0200] Perform holomorphic embedding construction on the active power equation based on the embedding factor to obtain the holomorphic embedding active power equation; among them, the holomorphic embedding active power equation includes the voltage phase embedding equation.

[0201] Perform holomorphic embedding construction on the reactive power equation based on the embedding factor to obtain the holomorphic embedding reactive power equation; among them, the holomorphic embedding reactive power equation includes the voltage phase embedding equation.

[0202] Construct the voltage magnitude embedding equation based on the embedding factor, the set value of the voltage magnitude of the PV node in the power grid data, and the set value of the voltage magnitude of the slack node.

[0203] Combine the holomorphic embedding active power equation, the holomorphic embedding reactive power equation, and the voltage magnitude embedding equation to obtain the holomorphic embedding power flow model.

[0204] Among them, when implementing this implementation method, by introducing the embedding factor to perform systematic holomorphic embedding on the active power equation, reactive power equation, and voltage magnitude constraint in the polar coordinate system, a structurally unified holomorphic embedding power flow model is constructed. This method innovatively embeds the voltage phase and magnitude into the complex variable domain respectively. By separating the embedding processes of the active / reactive power equation and the voltage magnitude constraint, it not only retains the physical intuitiveness of the polar coordinate form but also realizes the decoupled recursive solution mechanism of each variable. In particular, the set values of the voltage magnitudes of the PV node and the slack node are independently embedded, ensuring strict constraints on key operating parameters and effectively solving the problem of inaccurate voltage control in traditional methods under heavy load scenarios. This modular embedding method not only simplifies the derivation process of the high-order power series coefficients but also significantly improves the computational efficiency through a unified holomorphic embedding framework, providing a reliable guarantee for the rapid convergence and high-precision solution of the power flow of complex power systems.

[0205] As an alternative implementation, the specific way for the input unit 503 to input the auxiliary variables into the holomorphic embedding power flow model to obtain the initial node voltage magnitude and voltage initial phase can be as follows:

[0206] Expand the equation by embedding the voltage magnitude to obtain a voltage magnitude expansion function;

[0207] Expand the equation by embedding the voltage phase to obtain a voltage phase expansion function;

[0208] Based on the equation of embedding the voltage magnitude, construct auxiliary variables;

[0209] Input the embedding factor with a value of 0, the voltage magnitude expansion function, the voltage phase expansion function, and the auxiliary variables into the holomorphic embedding power flow model to obtain the initial node voltage magnitude and voltage initial phase.

[0210] Among them, implementing this implementation method constructs a systematic initial solution acquisition mechanism by expanding the functions of embedding the voltage magnitude and phase and introducing auxiliary variables to handle the non-linear terms. By setting the embedding factor to zero, the initial state solution process of the holomorphic embedding power flow model is directly simplified, enabling the initial node voltage magnitude and phase to be quickly determined through linearized equations. This method not only avoids the sensitivity dependence of the traditional iterative method on the initial value but also effectively solves the non-linear problem of the voltage reciprocal term in polar coordinates through the introduction of auxiliary variables, significantly improving the accuracy and stability of the initial solution.

[0211] As an alternative implementation, the specific way for the third construction unit 504 to construct the recurrence equation using the holomorphic embedding power flow model and auxiliary variables can be as follows:

[0212] Based on the impulse function, perform operations on the set values of the voltage magnitudes of the PV nodes and the set values of the voltage magnitudes of the slack nodes in the grid data to obtain a power series voltage magnitude coefficient equation;

[0213] Based on the power series voltage magnitude coefficient equation, the previously obtained power series voltage phase coefficient equation, and the previously obtained power series auxiliary variable coefficient equation, construct the active power equation to obtain an active power recurrence equation;

[0214] Based on the power series voltage magnitude coefficient equation, the power series voltage phase coefficient equation, and the power series auxiliary variable coefficient equation, construct the reactive power equation to obtain a reactive power recurrence equation;

[0215] Combine the power series voltage magnitude coefficient equation, the active power recurrence equation, and the reactive power recurrence equation to obtain a recurrence equation.

[0216] Among them, in implementing this implementation method, by introducing impulse functions to handle the voltage magnitude constraints of PV nodes and balanced nodes, a structured recursive equation system is constructed. This method innovatively integrates the voltage magnitude coefficient equation, phase coefficient equation, and auxiliary variable coefficient equation, and realizes the collaborative recursive solution of the active power equation and reactive power equation. Through the precise mathematical representation of the impulse function, strict constraints on the voltage magnitude of PV nodes are ensured, effectively solving the problem of voltage instability of traditional methods under extreme conditions. This modular recursive equation construction method not only simplifies the derivation process of high-order power series coefficients, but also significantly reduces the computational dimension through variable decoupling, enabling each order of recursion to only solve a linear equation system and greatly improving the computational efficiency.

[0217] As an alternative implementation method, the specific way for the solving unit 505 to solve the recursive equation order by order using the initial node voltage magnitude and voltage initial phase until the power series voltage magnitude coefficients and power series voltage phase coefficients converge can be as follows:

[0218] Set the recursion count to 0;

[0219] Solve the recursive equation order by order using the recursion count, initial node voltage magnitude, and voltage initial phase to obtain the active power and reactive power until the deviation value of the active power and reactive power is less than the preset convergence deviation, then it is determined that the obtained power series voltage magnitude coefficients and power series voltage phase coefficients converge;

[0220] Among them, in each solving process, add the current solving count to the recursion count to obtain a new recursion count; and solve the recursive equation based on the new recursion count, initial node voltage magnitude, and voltage initial phase to obtain the power series voltage magnitude coefficients and power series voltage phase coefficients; and solve the power series auxiliary variable coefficient equation based on the new recursion count and power series voltage magnitude coefficients to obtain the current power series auxiliary variable coefficients; and use the polar coordinate power flow equation to calculate the power series voltage magnitude coefficients, power series voltage phase coefficients, and current power series auxiliary variable coefficients to obtain the active power and reactive power.

[0221] Among them, in implementing this implementation method, by setting the recursion count and adopting an order-by-order solving mechanism, efficient convergence of the holomorphic embedded power flow model is realized. This method innovatively uses the initial voltage magnitude and phase as the recursion starting point, and ensures the systematicness and stability of the calculation process by dynamically updating the recursion count and cyclically solving each order of coefficients. Using the preset convergence deviation as the iteration termination condition not only ensures the calculation accuracy, but also avoids the problem of convergence failure that may occur in traditional iterative methods. In each recursive process, this method synchronously updates the voltage magnitude coefficients, phase coefficients, and auxiliary variable coefficients, and real-time checks the power deviation through the polar coordinate power flow equation, forming a closed-loop feedback mechanism.

[0222] The present invention can make each step of the calculation process closely connected, with a simple and efficient calculation logic, reduce unnecessary calculation overhead, and ultimately significantly improve the convergence of power flow calculation. In addition, the present invention can also greatly improve the recursive iteration efficiency on the premise of ensuring the accuracy of the power flow equation, provide a mathematical basis for the rapid power flow calculation of large-scale power grids, and reduce the consumption of computing resources at the same time. In addition, the present invention can also simplify the derivation process of high-order power series coefficients and significantly improve the calculation efficiency through a unified holomorphic embedding framework, providing a reliable guarantee for the rapid convergence and high-precision solution of the power flow of complex power systems. In addition, the present invention can also avoid the sensitivity dependence of the traditional iterative method on the initial value, and effectively solve the non-linear problem of the voltage reciprocal term in polar coordinate form by introducing auxiliary variables, significantly improving the accuracy and stability of the initial solution. In addition, the present invention can also improve the calculation efficiency. In addition, the present invention can ensure the calculation accuracy and avoid the convergence failure problem that may occur in the traditional iterative method.

[0223] Exemplary medium

[0224] After introducing the methods and devices of the exemplary embodiments of the present invention, next, refer to Figure 6 to describe the computer-readable storage medium of the exemplary embodiments of the present invention. Please refer to Figure 6 , which shows that the computer-readable storage medium is an optical disc 60, on which a computer program (i.e., a program product) is stored. When the computer program is run by a processor, it will implement each step recorded in the above method embodiments. For example, construct a polar coordinate power flow equation based on the power grid data read from the power grid system; perform holomorphic embedding construction on the polar coordinate power flow equation to obtain a holomorphic embedding power flow model; input the auxiliary variable into the holomorphic embedding power flow model to obtain the initial node voltage amplitude and voltage initial phase; use the holomorphic embedding power flow model and the auxiliary variable to construct a recursive equation; use the initial node voltage amplitude and voltage initial phase to solve the recursive equation order by order until the power series voltage amplitude coefficient and power series voltage phase coefficient obtained converge; use the power series voltage amplitude coefficient and power series voltage phase coefficient to perform power series summation respectively to obtain the node voltage amplitude and voltage phase; the specific implementation manners of each step will not be repeated here.

[0225] It should be noted that examples of computer-readable storage media may also include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory, or other optical and magnetic storage media, which will not be elaborated here one by one.

[0226] Exemplary computing device

[0227] After introducing the methods, apparatuses, and media of the exemplary embodiments of the present invention, next, reference is made to Figure 7 a computing device for power flow calculation in polar coordinate form according to the exemplary embodiments of the present invention.

[0228] Figure 7 The block diagram of an exemplary computing device 70 suitable for implementing the embodiments of the present invention is shown. The computing device 70 may be a computer system or a server. Figure 7 The shown computing device 70 is merely an example and should not impose any limitations on the functions and usage scope of the embodiments of the present invention.

[0229] As Figure 7 shown, the components of the computing device 70 may include but are not limited to: one or more processors or processing units 701, a system memory 702, and a bus 703 connecting different system components (including the system memory 702 and the processing unit 701).

[0230] The computing device 70 typically includes various computer system-readable media. These media can be any available media accessible by the computing device 70, including volatile and non-volatile media, removable and non-removable media.

[0231] The system memory 702 may include computer system-readable media in the form of volatile memory, such as random access memory (RAM) 7021 and / or cache memory 7022. The computing device 70 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, ROM 7023 may be used to read and write non-removable, non-volatile magnetic media ( Figure 7 not shown in the figure, commonly referred to as a "hard disk drive"). Although not shown in Figure 7 the figure, a disk drive for reading and writing removable non-volatile disks (such as "floppy disks") and an optical disk drive for reading and writing removable non-volatile optical disks (such as CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to the bus 703 through one or more data media interfaces. The system memory 702 may include at least one program product having a set of (e.g., at least one) program modules configured to perform the functions of the embodiments of the present invention.

[0232] A program / utilities 7025 having a set (at least one) of program modules 7024 can be stored in, for example, the system memory 702, and such program modules 7024 include, but are not limited to: an operating system, one or more application programs, other program modules, and program data, and an implementation of a network environment may be included in each or some combination of these examples. The program modules 7024 generally execute the functions and / or methods in the embodiments described in the present invention.

[0233] The computing device 70 can also communicate with one or more external devices 704 (such as a keyboard, a pointing device, a display, etc.). Such communication can be carried out through an input / output (I / O) interface 705. Moreover, the computing device 70 can also communicate with one or more networks (such as a local area network (LAN), a wide area network (WAN), and / or a public network, such as the Internet) through a network adapter 706. As Figure 7 shown, the network adapter 706 communicates with other modules (such as the processing unit 701, etc.) of the computing device 70 through a bus 703. It should be understood that although Figure 7 not shown in the figure, other hardware and / or software modules can be used in combination with the computing device 70.

[0234] The processing unit 701 executes various functional applications and data processing by running programs stored in the system memory 702. For example, based on grid data read from the power grid system, a polar coordinate power flow equation is constructed; a holomorphic embedding construction is performed on the polar coordinate power flow equation to obtain a holomorphic embedding power flow model; auxiliary variables are input into the holomorphic embedding power flow model to obtain the initial node voltage amplitude and the initial voltage phase; a recursive equation is constructed using the holomorphic embedding power flow model and the auxiliary variables; the recursive equation is solved step by step using the initial node voltage amplitude and the initial voltage phase until the power series voltage amplitude coefficients and the power series voltage phase coefficients obtained converge; power series summations are respectively performed using the power series voltage amplitude coefficients and the power series voltage phase coefficients to obtain the node voltage amplitude and the node voltage phase. The specific implementation manners of each step are not repeated here. It should be noted that although several units / modules or sub-units / sub-modules of the power flow calculation device based on the polar coordinate form are mentioned in the above detailed description, this division is merely exemplary and not mandatory. In fact, according to the embodiments of the present invention, the features and functions of two or more of the above-described units / modules can be embodied in one unit / module. Conversely, the features and functions of one unit / module described above can be further divided and embodied by multiple units / modules.

[0235] In the description of the present invention, it should be noted that the terms "first", "second", and "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0236] Those skilled in the art can clearly understand that for the convenience and conciseness of description, the specific working processes of the systems, devices, and units described above can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0237] Finally, it should be noted that the above embodiments are only specific embodiments of the present invention, used to illustrate the technical solutions of the present invention, rather than limiting them. The protection scope of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that any person skilled in the art within the technical scope disclosed by the present invention can still modify the technical solutions recorded in the foregoing embodiments or easily conceive of changes, or perform equivalent replacements for some of the technical features; and these modifications, changes, or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention and should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

[0238] In addition, although the operations of the method of the present invention are described in a specific order in the drawings, this does not require or imply that these operations must be performed in that specific order, or that all the shown operations must be performed to achieve the desired result. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step for execution, and / or one step may be decomposed into multiple steps for execution.

[0239] In an exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the foregoing method embodiments.

Claims

1. A power flow calculation method based on polar coordinate form, characterized in that, The method includes: Constructing a polar coordinate power flow equation based on the power grid data read from the power grid system; Performing a holomorphic embedding construction on the polar coordinate power flow equation to obtain a holomorphic embedding power flow model; Inputting the auxiliary variables into the holomorphic embedding power flow model to obtain the initial node voltage amplitude and the initial voltage phase; Using the holomorphic embedding power flow model and the auxiliary variables to construct a recursive equation; Using the initial node voltage amplitude and the initial voltage phase to solve the recursive equation order by order until the power series voltage amplitude coefficients and the power series voltage phase coefficients converge; Using the power series voltage amplitude coefficients and the power series voltage phase coefficients to perform power series summation respectively to obtain the node voltage amplitude and the voltage phase.

2. The power flow calculation method based on polar coordinates according to claim 1, characterized in that The constructing of the polar coordinate power flow equation based on the power grid data read from the power grid system includes: Constructing a node admittance matrix based on the power grid data read from the power grid system; Constructing an initial power flow equation based on the node admittance matrix; wherein, the initial power flow equation includes sine functions and cosine functions; Performing Taylor expansion on the sine functions and the cosine functions in the initial power flow equation to obtain the polar coordinate power flow equation.

3. The power flow calculation method based on the polar coordinate form according to claim 1, characterized in that The polar coordinate power flow equation includes an active power equation and a reactive power equation. The performing of the holomorphic embedding construction on the polar coordinate power flow equation to obtain a holomorphic embedding power flow model includes: Performing a holomorphic embedding construction on the active power equation based on the embedding factor to obtain a holomorphic embedding active power equation; wherein, the holomorphic embedding active power equation includes a voltage phase embedding equation; Performing a holomorphic embedding construction on the reactive power equation based on the embedding factor to obtain a holomorphic embedding reactive power equation; wherein, the holomorphic embedding reactive power equation includes the voltage phase embedding equation; Constructing a voltage amplitude embedding equation based on the embedding factor, the set value of the voltage amplitude of the PV node in the power grid data, and the set value of the voltage amplitude of the slack node; Combining the holomorphic embedding active power equation, the holomorphic embedding reactive power equation, and the voltage amplitude embedding equation to obtain a holomorphic embedding power flow model.

4. The method for power flow calculation based on polar coordinates according to claim 3, wherein The inputting of the auxiliary variables into the holomorphic embedding power flow model to obtain the initial node voltage amplitude and the initial voltage phase includes: Expanding the voltage amplitude embedding equation to obtain a voltage amplitude expansion function; Expanding the voltage phase embedding equation to obtain a voltage phase expansion function; Constructing auxiliary variables based on the voltage amplitude embedding equation; Inputting the embedding factor with a value of 0, the voltage amplitude expansion function, the voltage phase expansion function, and the auxiliary variables into the holomorphic embedding power flow model to obtain the initial node voltage amplitude and the initial voltage phase.

5. The power flow calculation method based on polar coordinates according to claim 4, wherein The using of the holomorphic embedding power flow model and the auxiliary variables to construct a recursive equation includes: Performing an operation on the set value of the voltage amplitude of the PV node in the power grid data and the set value of the voltage amplitude of the slack node based on the impulse function to obtain a power series voltage amplitude coefficient equation; Construct the active power equation based on the power series voltage amplitude coefficient equation, the pre-obtained power series voltage phase coefficient equation, and the pre-obtained power series auxiliary variable coefficient equation to obtain an active power recursive equation; Construct the reactive power equation based on the power series voltage amplitude coefficient equation, the power series voltage phase coefficient equation, and the power series auxiliary variable coefficient equation to obtain a reactive power recursive equation; Combine the power series voltage amplitude coefficient equation, the active power recursive equation, and the reactive power recursive equation to obtain a recursive equation.

6. The power flow calculation method based on polar coordinates according to claim 5, characterized in that The construction method of the power series auxiliary variable coefficient equation is specifically as follows: Construct a power series auxiliary variable coefficient equation using the auxiliary variable, the initial amplitude of the node voltage, and the power series voltage amplitude coefficient equation.

7. The power flow calculation method based on the polar coordinate form according to claim 6, characterized in that The step-by-step solution of the recursive equation using the initial amplitude of the node voltage and the initial voltage phase until the convergence of the power series voltage amplitude coefficient and the power series voltage phase coefficient obtained includes: Set the recursion count to 0; Solve the recursive equation step by step using the recursion count, the initial amplitude of the node voltage, and the initial voltage phase to obtain the active power and the reactive power until the deviation between the active power and the reactive power is less than a preset convergence deviation, then determine that the obtained power series voltage amplitude coefficient and the power series voltage phase coefficient converge; Wherein, in each solution process, add the current solution count to the recursion count to obtain a new recursion count; and solve the recursive equation based on the new recursion count, the initial amplitude of the node voltage, and the initial voltage phase to obtain the power series voltage amplitude coefficient and the power series voltage phase coefficient; and solve the power series auxiliary variable coefficient equation based on the new recursion count and the power series voltage amplitude coefficient to obtain the current power series auxiliary variable coefficient; and calculate the active power and the reactive power using the polar coordinate system power flow equation with the power series voltage amplitude coefficient, the power series voltage phase coefficient, and the current power series auxiliary variable coefficient.

8. The method for power flow calculation based on polar coordinates according to claim 3, characterized in that The active power equation of the polar coordinate system power flow equation is: Among them, P i is the active power injected into node i in the grid data; U i represents the node voltage amplitude of node i in the grid data, U j represents the node voltage amplitude of node j in the grid data, and N is the number of nodes in the grid data; G ij is the conductance part of the nodal admittance matrix; δ ij is the voltage phase difference between node i and node j; And, the reactive power equation of the polar coordinate system power flow equation is: Among them, Q i is the reactive power injected into node i in the grid data; B ij is the susceptance part of the nodal admittance matrix.

9. A power flow calculation device based on polar coordinate form, characterized in that, The device includes: A first construction unit for constructing a polar coordinate system power flow equation based on grid data read from a power grid system; A second construction unit for performing a holomorphic embedding construction on the polar coordinate system power flow equation to obtain a holomorphic embedding power flow model; An input unit for inputting an auxiliary variable into the holomorphic embedding power flow model to obtain the initial amplitude of the node voltage and the initial voltage phase; A third construction unit for constructing a recursive equation using the holomorphic embedding power flow model and the auxiliary variable; A solution unit for step-by-step solving the recursive equation using the initial amplitude of the node voltage and the initial voltage phase until the convergence of the power series voltage amplitude coefficient and the power series voltage phase coefficient obtained; A summation unit for performing power series summation using the power series voltage amplitude coefficient and the power series voltage phase coefficient respectively to obtain the amplitude of the node voltage and the voltage phase.

10. A computing device, characterized in that, The computing device includes: at least one processor, a memory, and an input / output unit; wherein, the memory is configured to store a computer program, and the processor is configured to call the computer program stored in the memory to execute the method according to any one of claims 1 to 8.

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