Modeling method of power system, calculation method of power flow model and electronic equipment

Abstract

The invention provides a modeling method of a power system, a calculation method of a power flow model and electronic equipment. According to the method, the combination of the ideal phase-shifting transformer and the common power transmission line is introduced, and the AD node is added, so that the problem of non-convergence possibly occurring in the power flow calculation of the power system in a classic full-pure embedding method is successfully solved. The phase-shifting transformer is split and AD nodes are introduced to serve as nodes with zero power, so that the stability and convergence of load flow calculation are ensured. On the basis, the reconstructed power flow model comprises multiple constraints such as a complex power balance equation of a PQ node and an AD node, an active power balance equation of a PV node, a voltage amplitude constraint equation and the like, and the calculation precision and reliability are further improved. The method can effectively deal with complex conditions in a large-scale power system, significantly improve convergence of load flow calculation, and provide powerful guarantee for stable operation of the power system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power systems, and in particular to a modeling method of a power system, a calculation method of a power flow model, and an electronic device. BACKGROUND

[0002] Power flow calculation in a power system is a basic analysis method for determining steady-state operating parameters of a power grid, and the goal is to solve the voltage amplitude, voltage phase angle of all nodes in the system, and the distribution of active power and reactive power of each branch under the condition of given network topology, generator output, load distribution, and control parameters.

[0003] The existing full pure embedding method (HEM) has the technical problem of convergence failure in a power system containing a large phase shift angle. SUMMARY

[0004] The purpose of the present application is to overcome the above technical deficiencies and provide a modeling method of a power system, a calculation method of a power flow model, and an electronic device to solve the technical problem of convergence failure of the existing full pure embedding method (HEM) in a power system containing a large phase shift angle in related technologies.

[0005] To achieve the above technical purpose, the present application adopts the following technical solutions: In a first aspect, the present application provides a modeling method of a power system, comprising: determining a target factor causing the full pure embedding method to fail to converge; based on the target factor, splitting a phase shift transformer carrying in a target power system into a combination of an ideal phase shift transformer and an ordinary transmission line, and introducing a new node as an AD node to construct a power model; wherein the AD node is a power node with a constant zero power injection; reconstructing a power flow model based on the power model to obtain a reconstructed power flow model; wherein the reconstructed power flow model includes a complex power balance equation of PQ nodes and AD nodes, an active power balance equation and a voltage amplitude constraint equation of PV nodes, a voltage amplitude constraint equation of a balanced node, and a phase shift constraint equation of the ideal phase shift transformer.

[0006] Further, the step of determining the target factor causing the full pure embedding method to fail to converge includes: using a power deviation-based detection method to determine the target factor causing the full pure embedding method to fail to converge; wherein the target factor includes numerical instability caused by a phase shift angle of a phase shift transformer exceeding a first threshold.

[0007] Further, the step of determining the target factor causing the non-convergence of the holomorphic embedding method in the power deviation based detection method comprises: performing the power flow calculation of the target power system by the holomorphic embedding method, recording the voltage update value of each node in the power series recursion process and calculating the oscillation amplitude of the voltage; calculating the power deviation value of each node; wherein the power deviation value is the difference between the actual injected power and the theoretical power flow of the node; if there are a pair of nodes that simultaneously satisfy the following conditions, it is determined that they are abnormal nodes connected by phase shift transformers: the power deviation value exceeds the second threshold value, the oscillation amplitude of the voltage exceeds the third threshold value, and the fluctuation trend is synchronized; determining that the pair of nodes are connected by phase shift transformers, and taking the phase shift angle of the phase shift transformer exceeding the first threshold value as the target factor.

[0008] Further, the representation of the complex power balance equation of the PQ node and the AD node is:

[0009] In the formula, N represents the total number of nodes in the system, Yik represents the element in the i-th row and the k-th column of the node admittance matrix, Vk represents the complex voltage at node k, Pi represents the complex power injected at node i, Pim represents the complex power flowing from node i to node m, and im represents the ideal phase shift transformer connected between node i and m, T represents the set of ideal phase shift transformers, PQ represents the set of PQ nodes, AD represents the set of AD nodes, N represents the number of nodes, Pim represents the complex voltage at node i, ; The active power balance equation and the voltage amplitude constraint equation of the PV node are represented as:

[0010] In the formula, Pim represents the complex voltage at node i, Yik represents the element in the i-th row and the k-th column of the node admittance matrix, Vk represents the complex voltage at node k, Pi represents the injected active power of the PV node i, Pim represents the sum of the active power of all ideal phase shift transformers connected to node i, Pim represents the real-time active power consumed by the ideal phase shift transformer itself, denotes the voltage magnitude of a PV node or a slack node, denotes a set of PV nodes, denotes the real part of a complex number; denotes the absolute value of a complex number.

[0011] Further, the voltage magnitude constraint equation of the slack node is denoted as:

[0012] In the formula, denotes a set of slack nodes; The phase shift constraint equation of the ideal phase-shifting transformer is denoted as:

[0013] In the formula, denotes a set of ideal phase-shifting transformers, denotes an ideal phase-shifting transformer connected between nodes i and m; denotes the voltage magnitude at the new node m, denotes the transformer ratio, and θshift denotes the transformer phase shift angle.

[0014] In a second aspect, the present application provides a calculation method of a power flow model of a power system, comprising: For the reconstructed power flow model, complex variables are embedded, and a full pure embedded form of the power flow model is constructed; wherein the reconstructed power flow model is the reconstructed power flow model described above; A preset solving algorithm is used to solve the full pure embedded form of the power flow model until the convergence precision is met, and the result parameters of each node in the target power system are obtained.

[0015] Further, the full pure embedded form of the power flow model comprises: a pure embedded form of the complex power balance equation of the PQ node and the AD node, a pure embedded form of the active power balance equation and the voltage magnitude constraint equation of the PV node, a pure embedded form of the voltage magnitude constraint equation of the slack node, a pure embedded form of the phase shift constraint equation of the ideal phase-shifting transformer, and a full pure function of the active and reactive power flowing through the ideal phase-shifting transformer.

[0016] Further, the pure embedded form of the complex power balance equation of the PQ node and the AD node is denoted as:

[0017] In the formula, ; The pure embedded form of the active power balance equation and the voltage magnitude constraint equation of the PV node is denoted as:

[0018] In the formula, ; The voltage amplitude constraint equation of the balanced node in the pure embedding form is expressed as:

[0019] The phase shift constraint equation of the ideal phase shift transformer in the pure embedding form is expressed as:

[0020] In the formula, ; The entire pure function of the active and reactive power flowing through the ideal phase shift transformer is expressed as:

[0021] In the formula, is expressed as an embedded complex variable, is the element in the i-th row and the k-th column of the series admittance matrix; is the parallel admittance at node i; is expressed as the entire pure function of the complex voltage at node k, is expressed as the conjugate of the complex power injected at node i, is expressed as the entire pure function of the active power flowing through the ideal phase shift transformer, is expressed as the entire pure function of the reactive power flowing through the ideal phase shift transformer, is expressed as the parallel admittance at node i, is expressed as the entire pure function of the complex voltage at node i, is expressed as the set of PQ nodes, is expressed as the set of AD nodes, is expressed as the entire pure function of the complex voltage conjugate at node i, is expressed as the injected active power at PV node i, is the imaginary unit, is the entire pure function of the reactive power at PV node i, is the set of PV nodes, and n represents the order of the power series; s is a complex variable embedding factor, and sn represents the complex variable embedding factor of the n-th order.

[0022] Further, the step of solving the entire pure embedding form of the power flow model by using a preset solving algorithm until a convergence precision is met to obtain the result parameters of each node in the target power system comprises: A corresponding recursive equation is constructed for the entire pure embedding form of the power flow model; wherein the recursive equation establishes a recursive relationship between the to-be-solved parameters by extracting the relationship between the high-order power series coefficients and the low-order power series coefficients; The recursive calculation is performed according to the recursive equation to obtain the result parameters of each node in the target power system; wherein the recursive equation comprises: The recursive equation of the PQ node and the AD node is represented as:

[0023] In the formula, is the current recursive order, is the n-th order series coefficient of the voltage of the node k, is the n-th order series coefficient of the active power loss of the phase-shifting transformer, is the n-th order series coefficient of the reactive power loss of the phase-shifting transformer, is the conjugate of the reciprocal term of the complex voltage Vi of the node i, is the conjugate of the n-th order coefficient of the reciprocal term of the voltage of the node i, is the low-order recursive serial number, represents that the AD node is positive and the non-AD node is negative; The recursive equation of the PV node and the balanced node is represented as:

[0024]

[0025] In the formula, represents the Kronecker delta function, represents the n-th order series coefficient of the reactive power of the PV node i, ; The recursive equation of the phase-shifting transformer is represented as:

[0026] In the formula, represents the n-th order coefficient of the voltage of the original node i of the phase-shifting transformer, represents the n-th order coefficient of the voltage of the new node m of the phase-shifting transformer, ; The unified recursive equation is represented as:

[0027] In the formula, A is a recursive matrix required for the recursive calculation and remains constant in the process of the recursive calculation; x[n] is the n-th order series coefficient to be solved; is the right side term of the recursive equation, which is calculated by the power series coefficients smaller than the n-th order.

[0028] ​​In a third aspect, the present application provides an electronic device, comprising: a memory, and one or more processors in communication connection with the memory; the memory has stored instructions executable by the one or more processors, and the instructions are executed by the one or more processors to enable the one or more processors to implement the method described above.

[0029] Advantages: The present application successfully solves the non-convergence problem that may occur in the classical full-pure embedding method in power system load flow calculation by introducing the combination of ideal phase-shifting transformers and ordinary power transmission lines and adding AD nodes. By splitting the phase-shifting transformers and introducing the AD nodes as nodes with zero power, the stability and convergence of the load flow calculation are ensured. On this basis, the reconstructed load flow model contains multiple constraints such as the complex power balance equations of PQ nodes and AD nodes, the active power balance equations of PV nodes, and the voltage amplitude constraint equations, further improving the calculation accuracy and reliability. This method can effectively deal with complex situations in large-scale power systems, significantly improve the convergence of load flow calculation, and provide a strong guarantee for stable operation of power systems. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is a flowchart of a modeling method of a power system provided by an embodiment of the present application; Figure 2 is a schematic diagram of an improved phase-shifting transformer load flow calculation model provided by an embodiment of the present application; Figure 3 is a schematic diagram of the node voltage amplitude update value results of an example case1888rte system under the classical full-pure embedding method provided by an embodiment of the present application; Figure 4 is a schematic diagram of a comparison table of two classical full-pure embedding forms provided by an embodiment of the present application; Figure 5 is a schematic diagram of a comparison table of the first six-order power series coefficients of node 7 of three methods (phase-shifting angle is 2°) provided by an embodiment of the present application; Figure 6 is a schematic diagram of a comparison table of the number of phase-shifting transformers and the size of phase-shifting angles of multiple example systems provided by an embodiment of the present application; Figure 7 is a schematic diagram of a comparison table of the calculation efficiency and convergence of the method and the NR method provided by an embodiment of the present application. DETAILED DESCRIPTION

[0031] In order for those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be described clearly and completely in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should be within the scope of protection of the present application.

[0032] In the related art, with the transformation of global energy structure and the development of low-carbon economy, modern power systems have begun to massively access new energy, direct current transmission and various flexible regulation devices (such as phase-shifting transformers and static synchronous compensators, etc.). These emerging devices optimize the transmission and distribution of electricity through efficient power electronic technology, and enhance the flexibility and stability of the power grid. However, with the widespread access of these devices, the complexity of the power system has increased significantly, especially in the face of the volatility and uncertainty of large-scale renewable energy, the demand for accurate analysis of the power system has become increasingly urgent.

[0033] Under such circumstances, traditional power flow calculation methods, such as the Newton-Raphson method (NR method), are inefficient due to their sensitivity to initial values and the need to recalculate the Jacobian matrix at each iteration, and have difficulty meeting the dual demands of real-time and accuracy of modern power grids. In contrast, holomorphic embedding method (HEM) as a non-iterative method, by using the analytic continuation of complex variables, can theoretically avoid the dependence on initial values and support parallel recursive calculation, so it is considered an important development direction for the next generation of power flow calculation methods.

[0034] Holomorphic embedding method (HEM) converts the power flow equations of the power system into an analytic function on the complex plane, and recursively approximates the steady-state solution using power series expansion. In theory, this method can stably solve the power flow problem of the power system without relying on initial values. However, actual large-scale system tests show that the traditional classic holomorphic embedding method (CHEM) has a serious convergence failure problem when dealing with power systems containing large phase-shifting angles.

[0035] For example, in the 1888-node power system in Europe, when the phase-shifting angle exceeds several degrees, the convergence rate of CHEM decreases, and even convergence failure occurs. That is, the standard system (without phase-shifting transformer) can achieve 100% convergence rate when the phase-shifting angle is 0 degrees, but once the phase-shifting transformer is introduced, especially when the phase-shifting angle is greater than a certain value, the convergence of CHEM decreases sharply.

[0036] The root cause of this convergence problem lies in the deficiency of the traditional phase-shifting transformer model. The presence of the phase-shifting angle significantly increases the value of the right-hand side of the matrix, which is equivalent to connecting a much larger admittance to the node than the actual situation, deviating from the true operating state of the power grid, and thus triggering the deterioration of convergence.

[0037] In the embodiment, the target factor causing the non-convergence of the holomorphic embedding method can be numerical instability caused when the phase-shifting angle of the phase-shifting transformer exceeds the first threshold value.

[0038] As shown in Figure 1 , Figure 2 and Figure 3 , to solve the above technical problems, the embodiment provides a modeling method of a power system, comprising: Step S12: determining a target factor causing the non-convergence of the holomorphic embedding method.

[0039] In the embodiment, a detection method based on power deviation can be used to determine the target factor causing the non-convergence of the holomorphic embedding method; wherein the target factor includes numerical instability caused when the phase-shifting angle of the phase-shifting transformer exceeds the first threshold value.

[0040] It should be noted that in the power system, the updating process of the node voltage amplitude is usually a smooth convergence process. However, in the case1888rte system, the voltage amplitude updating process of the node 422 and the node 982 shows a dramatic fluctuation. Figure 3 The results show that the voltage amplitude fluctuation amplitudes of the two nodes are almost the same, showing obvious synchronization characteristics. Generally, the phenomenon of excessive voltage amplitude fluctuation can be a signal of non-convergence in power flow calculation, which is worth special attention.

[0041] In the power system, nodes that are adjacent in physical location often influence each other, but if there is no direct electrical connection, their voltage fluctuations will not be completely synchronized. The high synchronization of voltage fluctuations between the node 422 and the node 982 indicates that there is a certain direct electrical connection between the two nodes. According to the configuration of the system, the node 422 and the node 982 are connected through a phase-shifting transformer (PST). The phase-shifting transformer controls the direction of power flow by adjusting the phase difference between voltages, thereby affecting the stability of the power grid. In this power system, the phase-shifting transformer is the only device connecting the two nodes. Therefore, the abnormal fluctuation of the node voltage amplitude is closely related to the connection between the two nodes through the phase-shifting transformer.

[0042] It can be appreciated that the working principle of the phase-shifting transformer is mainly to change the voltage phase difference by adjusting the phase-shifting angle. This process is highly nonlinear, and the power-voltage equation of the phase-shifting transformer includes complex exponential terms, which makes the model sensitive in numerical calculation. When performing power flow calculation, if the model of the phase-shifting transformer fails to accurately reflect these nonlinear characteristics, it may cause the numerical calculation to oscillate in convergence. This instability directly leads to a sharp fluctuation in the voltage amplitude, ultimately causing the power flow calculation to diverge.

[0043] Holomorphic Embedding Method (HEM) is a non-iterative power flow calculation method, which expands the voltage function through complex variables, often relying on the convergence of power series for solution. In the Holomorphic Embedding Method, the voltage update process is adjusted by continuously calculating the power series coefficients. For linear models, the power series coefficients usually decay quickly, and the convergence process is relatively stable. However, if strong nonlinear terms (complex exponential terms) such as phase-shifting transformers are introduced into the model, the decay of power series coefficients becomes very slow, and even diverges, showing high-order coefficient oscillation. This oscillation will manifest in the voltage update process, showing a synchronous fluctuation in the node voltage amplitude.

[0044] Newton-Raphson (NR) method is a commonly used iterative power flow calculation method. When encountering convergence problems, it often directly diverges and does not provide oscillation data in the intermediate process. Therefore, in the NR method, if the calculation does not converge, the system will directly report an error or fail to obtain a solution, and the oscillation process cannot be displayed. In the Holomorphic Embedding Method, due to its recursive nature, the voltage amplitude update process is more explicit, and any instability will be exposed, especially when high-order power series coefficients cannot decay, the oscillation phenomenon will be more pronounced.

[0045] Therefore, the inaccurate modeling of the phase-shifting transformer is the root cause of the divergence of the power flow calculation. The nonlinear characteristics of the phase-shifting transformer are highly consistent with the sensitivity of the Holomorphic Embedding Method, and the incorrect handling of nonlinear terms in the modeling of the phase-shifting transformer often leads to a sharp oscillation in the voltage amplitude, making the power flow calculation unable to converge. By comparing the performance of the NR method and the Holomorphic Embedding Method, it can be seen that the Holomorphic Embedding Method has a unique advantage in the explicit display of oscillation phenomena, which provides strong evidence for the potential problem of phase-shifting transformer modeling.

[0046] Therefore, it can be appreciated that the abnormal fluctuation of the voltage amplitude between node 422 and node 982, as well as the characteristics of the connection between the two nodes through the phase-shifting transformer, show that the modeling of the phase-shifting transformer may be the cause of the divergence of the power flow calculation. The interaction between the nonlinear terms in the phase-shifting transformer model and the convergence requirement of the Holomorphic Embedding Method further exacerbates the voltage amplitude fluctuation, leading to instability in the calculation.

[0047] Step S14: based on the target factor, the phase-shifting transformer carried in the target power system is split into a combination of an ideal phase-shifting transformer and a general power transmission line, and a new node is introduced as an AD node to construct a power model; wherein the AD node is a power node with a constant zero injected power.

[0048] As shown in Figure 2 In the embodiment, first, a new node m can be introduced between the original connected node i and the target node n of the phase-shifting transformer. The node m acts as a virtual node to isolate the nonlinear impact of the phase-shifting transformer and provide a simplified power system model for subsequent calculation. The introduction of the new node m not only helps to separate the function of the phase-shifting transformer, but also effectively reduces the unstable factors in the calculation.

[0049] Then, the phase-shifting transformer originally connected to the node i and the node n can be split into two devices, namely an ideal phase-shifting transformer and a general power transmission line. Specifically, the ideal phase-shifting transformer can be connected to the node i and the new node m, and is specifically used to describe the voltage transformation relationship. In this model, the ideal phase-shifting transformer can be used to adjust the voltage phase difference and does not involve the resistance and reactance of the line. The general power transmission line can be connected to the new node m and the target node n, and retains the resistance, reactance and susceptance parameters of the line on which the original phase-shifting transformer is connected, ensuring that the original system electrical characteristics are retained.

[0050] In the embodiment, the new node can be defined as an AD node (Augmented Device Node). Specifically, the active power and reactive power of the node are both zero, and the voltage amplitude and voltage phase angle of the node are to be solved variables. It should be noted that the new node can be classified as a PQ node, but unlike the conventional PQ node, the AD node has a constant zero power and is intended to provide a voltage reference point for the system without participating in actual power flow.

[0051] In the embodiment, it can be understood that the introduction of the AD node does not affect the power balance of the entire power system, and only serves as a virtual node to supplement the nonlinear impact of the phase-shifting transformer, thereby helping the power system to better stabilize the convergence when performing power flow calculation. In this way, the numerical instability caused by the nonlinear characteristics of the phase-shifting transformer in the original system is effectively isolated, avoiding the situation of excessive voltage amplitude fluctuation and convergence failure.

[0052] Step S16: reconstructing a power flow model based on the power model, to obtain a reconstructed power flow model; wherein the reconstructed power flow model comprises complex power balance equations of PQ nodes and AD nodes, active power balance equations and voltage amplitude constraint equations of PV nodes, voltage amplitude constraint equations of slack nodes, and phase shift constraint equations of the ideal phase-shifting transformers.

[0053] In the embodiment, the injected active power and reactive power of the PQ node are known quantities, and the voltage amplitude and phase angle are unknown quantities. The PQ node can represent a load node, which can be a residential load.

[0054] In the embodiment, the PV node can be a voltage control node and can be used to represent a power source with automatic voltage regulation capability. The injected active power and voltage amplitude of the PV node are known quantities, and the injected reactive power and voltage phase angle are unknown quantities.

[0055] In the embodiment, the voltage amplitude and phase angle of the slack node are known quantities, and the injected active power and reactive power are unknown quantities.

[0056] In the embodiment, the AD node is a newly added virtual node, and its function is to ensure that the nonlinear effects of the phase-shifting transformer are correctly reflected. At this node, the injected power is set to zero, and the voltage amplitude and phase angle are variables to be solved. The complex power balance equations of this node and other nodes ensure the balance of system power flow and avoid the instability caused by the phase-shifting transformer.

[0057] The embodiment successfully solves the non-convergence problem that may occur in the classical full-pure embedding method in power system power flow calculation by introducing the combination of ideal phase-shifting transformers and ordinary transmission lines and adding AD nodes. By splitting the phase-shifting transformer and introducing the AD node as a node with zero power, the stability and convergence of the power flow calculation are ensured. On this basis, the reconstructed power flow model contains multiple constraints such as complex power balance equations of PQ nodes and AD nodes, active power balance equations and voltage amplitude constraint equations of PV nodes, etc., further improving the calculation accuracy and reliability. This method can effectively deal with complex situations in large-scale power systems, significantly improve the convergence of power flow calculation, and provide a strong guarantee for stable operation of power systems.

[0058] In some embodiments, the step of determining the target factor that causes the full-pure embedding method to not converge comprises: Step S122: determining the target factor that causes the full-pure embedding method to not converge by using a detection method based on power deviation; wherein the target factor includes numerical instability caused when the phase shift angle of the phase-shifting transformer exceeds a first threshold value.

[0059] In the embodiment, the first threshold value can be represented as a critical point found by the power deviation detection method during the simulation process, indicating that when the phase-shifting angle of the phase-shifting transformer exceeds this value, the power flow calculation of the power system will exhibit numerical instability. Specifically, after the phase-shifting angle exceeds the first threshold value, the power deviation of each node in the power system will suddenly jump from a normal magnitude to an abnormal magnitude. This sudden change indicates that the power flow of the power system begins to fluctuate significantly and cannot maintain a normal and stable state. At the same time, the change in voltage amplitude presents a significant synchronous oscillation phenomenon, i.e., the voltage amplitude fluctuations of multiple nodes in the system are synchronized and significantly increased. This indicates that the stability of the system is destroyed and the normal distribution of the voltage is disturbed, resulting in the inability of the Holomorphic Embedding Method (HEM) to converge.

[0060] It can be understood that the first threshold value is a regular inflection point identified according to the actual system performance during the simulation process. By analyzing the change pattern of the power deviation and the voltage fluctuation in the system, it can be found that when the phase-shifting angle exceeds a certain specific value, the calculation stability of the system changes significantly, and this specific value is the first threshold value.

[0061] It can also be understood that the specific value of the first threshold value is not fixed but varies with the characteristics of different power systems, such as system configuration, number of nodes, phase-shifting transformer parameters, etc.

[0062] This embodiment effectively identifies the target factor causing the Holomorphic Embedding Method to not converge by introducing a power deviation-based detection method, especially the numerical instability problem caused when the phase-shifting angle of the phase-shifting transformer exceeds the threshold value. Through this detection method, the change in power deviation can be monitored in real time during the power flow calculation, thereby accurately locating the key factor causing the calculation to not converge. Especially in complex power systems, the abnormal voltage amplitude fluctuation caused by the nonlinear characteristics of the phase-shifting transformer can be found in time, providing a clear basis for subsequent optimization and adjustment. This method improves the stability and accuracy of power system power flow calculation, ensuring the reliability of the Holomorphic Embedding Method in practical applications, and providing more effective technical support for the safety analysis and dispatch of large-scale power grids.

[0063] In some embodiments, the step of determining the target factor causing the Holomorphic Embedding Method to not converge using the power deviation-based detection method includes: Step S1222: performing power flow calculation of the Holomorphic Embedding Method on the target power system, recording the voltage update value of each node in the power series recursion process and calculating the oscillation amplitude of the voltage.

[0064] In the embodiment, the full-pure embedding method can be applied to the target power system for power flow calculation. The full-pure embedding method updates the voltage of each node through power series recursion. At each iteration, the updated value of the node voltage is calculated, and the oscillation amplitude of the voltage is calculated according to the value. The voltage oscillation amplitude can represent the amplitude of the change of the node voltage during the recursion process, which can represent rapid fluctuations or unstable behavior of the voltage. By recording the voltage update value and the oscillation amplitude, the stability of the power system can be monitored, and the basic data for subsequent analysis can be provided. That is, during the power flow calculation process, the voltage update of each node can be recorded, and the voltage value of each node can be compared to determine the oscillation amplitude (i.e., the fluctuation amplitude of the voltage value) in the voltage update process.

[0065] Step S1224: calculating the power deviation value of each node; wherein the power deviation value is the difference between the actual injected power and the theoretical power flow of the node.

[0066] In the embodiment, the power deviation value of each node can be calculated. The power deviation can represent the difference between the actual injected power and the theoretical power flow of the node. The actual injected power is the power calculated according to the operating conditions and voltage of the power system, while the theoretical power flow is the power calculated according to the power flow model of the system. The power deviation reflects the difference in power flow of the node and is an important indicator for measuring whether the power flow calculation converges. That is, for each node, the actual injected power and the theoretical power flow are compared, and the difference between them, i.e., the power deviation, is calculated.

[0067] Step S1226: if there are nodes that simultaneously satisfy the following conditions, the nodes are determined to be abnormal nodes connected by phase-shift transformers: the power deviation value exceeds the second threshold value, the oscillation amplitude of the voltage exceeds the third threshold value, and the fluctuation trend is synchronized.

[0068] In the embodiment, all nodes can be screened, and nodes with power deviation values exceeding the second threshold value and voltage oscillation amplitudes exceeding the third threshold value can be screened. If the voltage oscillation fluctuation trends of these nodes are synchronized, these nodes can be determined to be abnormal nodes. It should be noted that it can be further determined whether these abnormal nodes are connected by phase-shift transformers. It can be understood that the phase-shift transformer is an important device in the power system, which is used to adjust the phase difference of the voltage, but the nonlinear characteristics of the phase-shift transformer can cause abnormal power flow and voltage distribution in the system.

[0069] In the embodiment, the second threshold value can be represented as a critical value of the power deviation value, when the power deviation of the node exceeds the threshold value, indicating that the node has abnormal power flow or calculation error. The second threshold can be a value determined according to simulation analysis and historical data, representing a critical point at which the power deviation value in the power system abnormally increases. If the power deviation exceeds the second threshold value, it indicates that the power flow of the node is abnormal, which can be caused by the non-linear effect of the phase-shifting transformer or other external factors.

[0070] In the embodiment, the third threshold value can be represented as a critical value of the voltage oscillation amplitude, indicating that when the voltage oscillation amplitude of the node exceeds the threshold value, the stability of the power system is threatened, which can lead to the non-convergence of the power flow calculation. Similarly, the third threshold value can also be a value determined according to simulation analysis and historical data.

[0071] Step S1228: Determine that the pair of nodes are connected through a phase-shifting transformer, and that the phase-shifting angle of the phase-shifting transformer exceeds the first threshold value as the target factor.

[0072] In the embodiment, once it is identified that the pair of nodes are connected through a phase-shifting transformer, the phase-shifting angle of the phase-shifting transformer can be detected, and if the phase-shifting angle exceeds the first threshold value, it can be determined that the phase-shifting transformer is a key factor leading to the numerical instability of the power system.

[0073] The embodiment effectively identifies the target factor leading to the non-convergence of the full pure embedding method by combining the power deviation detection method and the voltage oscillation analysis. Specifically, by recording the voltage update value and the oscillation amplitude of the node in the power series recursion process, the abnormal fluctuations caused by the non-linear effect of the phase-shifting transformer in the power system can be accurately captured. When the power deviation value of a pair of nodes in the power system exceeds the second threshold value, and the voltage oscillation amplitude exceeds the third threshold value and the fluctuation trend is synchronized, it can be determined that these nodes are abnormal nodes connected through a phase-shifting transformer. At this time, further confirmation of the phase-shifting angle of the phase-shifting transformer exceeding the first threshold value as the root cause of the system instability. Through this method, the key factor affecting the convergence of the full pure embedding method can be accurately identified, thereby providing a scientific basis for system optimization, improving the stability and accuracy of the power flow calculation, and ensuring the reliability and accuracy of the power system under complex conditions.

[0074] In some embodiments, the representation of the complex power balance equation of the PQ node and the AD node is:

[0075] In the formula, represents the total number of nodes in the system, represents the element in the i-th row and the k-th column of the node admittance matrix, the complex voltage at node k, the complex power injected at node i, the complex power flowing from node i to node m, im represents an ideal phase-shifting transformer connected between node i and m, represents a set of ideal phase-shifting transformers, represents a set of PQ nodes, represents a set of AD nodes, represents the conjugate of a complex number, N represents the number of nodes, represents the conjugate of the complex voltage at node i, ; The active power balance equation and the voltage magnitude constraint equation of the PV node are represented as:

[0076] In the formula, represents the conjugate of the complex voltage at node i, represents the element in the i-th row and the k-th column of the node admittance matrix, the complex voltage at node k, represents the injected active power of the PV node i, represents the sum of the active power of all ideal phase-shifting transformers connected to node i, represents the real-time active power consumed by the ideal phase-shifting transformer itself, represents the specified voltage magnitude of the PV node or the slack node, represents a set of PV nodes, represents the real part of a complex number; represents the absolute value of a complex number.

[0077] In this embodiment, the power flow and voltage change between nodes are accurately described through the complex power balance equation, reducing errors in calculation. Through reasonable voltage magnitude constraints and phase-shifting constraints, the system can better converge under complex conditions, avoiding oscillation and divergence in traditional methods. This embodiment can handle complex devices such as phase-shifting transformers in large-scale power systems, especially when the system contains multiple nonlinear elements, still maintaining good stability and convergence performance. Through the above improvements, the accuracy and stability of power system load flow calculation have been significantly improved, especially when facing large-scale power grids and complex devices, providing more reliable calculation results for system optimization and real-time scheduling.

[0078] In some embodiments, the voltage magnitude constraint equation of the slack node is represented as:

[0079] In the formula, represents a set of slack nodes; The phase-shifting constraint equation of the ideal phase-shifting transformer is expressed as:

[0080] In the formula, denotes a set of ideal phase-shifting transformers, denotes an ideal phase-shifting transformer connected between nodes i and m; denotes a voltage amplitude at the new node m, denotes a transformer ratio, and θshift denotes a transformer phase-shifting angle.

[0081] In this embodiment, on the one hand, by introducing the ideal phase-shifting transformer and the voltage amplitude constraint, the calculation oscillation and instability phenomenon caused by the nonlinear characteristics of the phase-shifting transformer are avoided, and the stability of the system is improved. On the other hand, by accurately constraining the node voltage amplitude and phase angle, the voltage update in the power system flow calculation is more accurate, which is helpful for the fine control of system operation. On the other hand, this embodiment can effectively handle complex power systems containing nonlinear elements such as phase-shifting transformers, especially in multi-node and multi-device systems, and can maintain high calculation accuracy and convergence performance.

[0082] The embodiment provides a calculation method of a power system flow model, including: Step S22: embedding complex variables and constructing a full pure embedded form of the power flow model for the reconstructed power flow model; wherein the reconstructed power flow model is the reconstructed power flow model provided in the above embodiment; Step S24: solving the full pure embedded form of the power flow model by using a preset solving algorithm until the convergence precision is met, to obtain the result parameters of each node in the target power system.

[0083] In this embodiment, the power flow model in the full pure embedded form can be solved by using a power series recursive algorithm until the convergence precision is met, to obtain the result parameters of each node in the target power system.

[0084] In this embodiment, the result parameters can include voltage amplitude, voltage phase angle, power flow, or voltage deviation, etc.

[0085] The embodiment significantly improves the accuracy and convergence of power flow calculation by embedding the power flow model of the power system into complex variables and converting it into a holomorphic embedding form combined with a preset solving algorithm. First, the reconstructed power flow model can more accurately describe the voltage and power flow in the power system by introducing complex variables, especially when dealing with complex devices such as phase-shift transformers, avoiding nonlinear errors in traditional methods. Second, by using the holomorphic embedding form, the method fully utilizes the complex analysis theory to ensure the power series in the power flow calculation process to converge stably, thereby reducing the oscillation and instability in the calculation. By adopting the preset solving algorithm, the system can efficiently solve the holomorphic embedding form of the power flow model and obtain the accurate result parameters of each node in the target power system under the condition of meeting the convergence accuracy. This method effectively improves the calculation efficiency, ensures that the voltage amplitude, phase angle and other key parameters can be quickly and accurately obtained in large-scale power systems, and ensures the stable operation and optimal scheduling of the power system. The embodiment solves the convergence problem in traditional power flow calculation by accurate modeling and efficient solving, especially when dealing with complex power systems, it can provide more reliable and fast calculation results, and has significant engineering application value.

[0086] In some embodiments, the holomorphic embedding form of the power flow model includes: a complex power balance equation of PQ nodes and AD nodes in a holomorphic embedding form, an active power balance equation and a voltage amplitude constraint equation of PV nodes in a holomorphic embedding form, a voltage amplitude constraint equation of a balanced node in a holomorphic embedding form, a phase shift constraint equation of the ideal phase-shift transformer in a holomorphic embedding form, and a holomorphic function of active and reactive power flowing through the ideal phase-shift transformer.

[0087] The embodiment significantly improves the stability and accuracy of the calculation by applying the holomorphic embedding form to the power flow model of the power system. By introducing complex power balance equations, voltage amplitude constraint equations and phase shift constraint equations, the influence of various types of nodes (such as PQ nodes, PV nodes, balanced nodes) and ideal phase-shift transformers is accurately modeled, thereby effectively avoiding numerical instability problems caused by nonlinear devices in traditional calculations. In addition, the power flowing through the phase-shift transformer is processed using a holomorphic function form, making the system calculation more accurate, especially when facing large-scale and complex power systems, still ensuring high convergence and calculation efficiency. This method improves the reliability of power system power flow calculation and provides a more accurate basis for system optimization and scheduling.

[0088] In some embodiments, the complex power balance equation of PQ nodes and AD nodes in a holomorphic embedding form is represented as:

[0089] In the formula, ; The active power balance equation and the voltage magnitude constraint equation of the PV node in the pure embedding form are expressed as:

[0090] In the formula, ; The voltage magnitude constraint equation of the balance node in the pure embedding form is expressed as:

[0091] The phase shift constraint equation of the ideal phase shift transformer in the pure embedding form is expressed as:

[0092] In the formula, ; The entire pure function of the active and reactive power flowing through the ideal phase shift transformer is expressed as:

[0093] In the formula, is expressed as an embedded complex variable, is the element in the i-th row and the k-th column of the series admittance matrix; is the parallel admittance at node i; is expressed as the entire pure function of the complex voltage at node k, is expressed as the conjugate of the complex power injected at node i, is expressed as the entire pure function of the active power flowing through the ideal phase shift transformer, is expressed as the entire pure function of the reactive power flowing through the ideal phase shift transformer, is expressed as the parallel admittance at node i, is expressed as the entire pure function of the complex voltage at node i, is expressed as the set of PQ nodes, is expressed as the set of AD nodes, is expressed as the entire pure function of the conjugate of the complex voltage at node i, is expressed as the injected active power of the PV node i, is the imaginary unit, is the entire pure function of the reactive power of the PV node i, is the set of PV nodes, and n represents the order of the power series; s is a complex variable embedding factor, and sn represents the complex variable embedding factor of the n-th order.

[0094] In some embodiments, the step of solving the entire pure embedding form of the power flow model by using a preset solving algorithm until a convergence precision is met to obtain the result parameters of each node in the target power system comprises: For the fully embedded power flow model, a corresponding recursive equation is constructed; wherein, the recursive equation establishes a recursive relationship between the parameters to be solved by extracting the relationship between the coefficients of higher-order power series and the coefficients of lower-order power series. For the recursive equation, recursive calculations are performed to obtain the result parameters for each node in the target power system; wherein, the recursive equation includes: The recursive equations for nodes PQ and AD are expressed as follows:

[0095] In the formula, Let this be the current recursion order. For the nth power series coefficients of the voltage at node k, ... These are the coefficients of the nth power series of active power losses in a phase-shifting transformer. The coefficients of the nth power series of reactive power loss in a phase-shifting transformer are given. Let Vi be the conjugate of the reciprocal of the complex voltage Vi at node i. The reciprocal of the voltage at node i The Conjugate of order coefficients, The lower-order recursion sequence number. This means that nodes with AD are positive and nodes without AD are negative. The recurrence equations for PV nodes and equilibrium nodes are expressed as follows:

[0096]

[0097] In the formula, Represented as the Kronecker delta function, Let the coefficients of the nth power series of reactive power at PV node i be represented. ; The recursive equation for a phase-shifting transformer is expressed as follows:

[0098] In the formula, This represents the nth-order coefficient of the voltage at primary node i of the phase-shifting transformer. This represents the nth-order coefficient of the voltage at the newly added node m of the phase-shifting transformer. ; The unified recursive equation is expressed as:

[0099] In the formula, A is the recursive matrix required for recursive calculation, which remains constant during the recursive calculation process; x[n] is the coefficient of the nth power series to be calculated. For the right side term of the recursive equation, the term is calculated from the power series coefficients of order less than n.

[0100] In one specific embodiment, a holomorphic embedding method based on improved modeling of phase-shift transformers is provided. The method first introduces a power deviation detection method to identify the key factors that cause the classical holomorphic embedding method to diverge. Based on this, an improved phase-shift transformer model and its corresponding holomorphic embedding form are constructed, and the calculation steps for the initial solution and high-order power series are derived.

[0101] Terminology explanation: Holomorphic embedding method: Holomorphic Embedding Method (HEM), is a non-iterative algorithm for power system power flow calculation.

[0102] Taylor expansion: Taylor Expansion (TE), refers to a mathematical method of approximating a function at a certain point using power series based on the derivative information at that point.

[0103] Power flow calculation: Power Flow Calculation (PFC), refers to the numerical calculation process of solving the amplitude and phase angle of each node voltage, as well as the line power flow and power distribution in the entire system based on the known partial node voltage 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.

[0104] Newton-Raphson algorithm: Newton-Raphson (NR), is an iterative algorithm for solving nonlinear equations.

[0105] Per unit: per unit (p.u.), is a numerical marking method commonly used in power system and engineering calculations, representing the relative value of each physical quantity and parameter, dimensionless.

[0106] Power flow calculation is a fundamental tool for power system planning and operation analysis. Power flow calculation is essentially the solution of high-dimensional nonlinear equations. The most commonly used power flow calculation method in industry is the iterative Newton-Raphson (NR) method. However, this method has the following shortcomings: 1) it is sensitive to the selection of initial values, and unreasonable initial values may lead to slow convergence or even non-convergence; 2) the Jacobian matrix needs to be regenerated and the correction equation needs to be calculated in each iteration, which leads to slow calculation speed of the NR method; 3) when the power flow does not converge, it is not clear whether the power flow itself has no solution or the power flow has a solution but the power flow solution has not been solved. With the expansion of the scale of the power system and the large-scale access of power electronic devices, the operation mode of the power system is complex and variable, and the power flow does not converge more seriously, which challenges the reliability of the security and stability analysis of the power system. Therefore, it is urgent to propose a more reliable power flow calculation method.

[0107] In view of the above problems of the traditional iterative power flow calculation method, the related technology proposes a recursive power flow calculation method, namely the Holomorphic Embedding Method (HEM) power flow algorithm. This method is based on complex analysis theory, embeds complex variables in the power flow equation, and constructs the variables to be solved as holomorphic functions. Then, according to the expansion property of holomorphic functions, the power flow solution is converted into recursively obtaining the power series coefficients of holomorphic functions. This method does not need to provide initial values and form the Jacobian matrix. The holomorphic embedding method can guarantee convergence to a runnable solution when the power flow exists, and give a clear numerical oscillation signal when the power flow has no solution.

[0108] When the traditional iterative power flow calculation method does not converge, the voltage results obtained by the calculation often deviate seriously from the actual operation state of the system, and it is difficult to provide effective reference information for subsequent power flow convergence adjustment. As a recursive power flow calculation method, the holomorphic embedding method overcomes the initial value dependence problem to some extent and shows excellent convergence performance in a large number of existing researches. However, due to factors such as numerical calculation accuracy, embedding form construction and system characteristics, the holomorphic embedding method may still fail to converge in actual application. For example, in some system examples with large node size (such as case1888rte and case13659pegase), the classical holomorphic embedding method fails to converge. At present, in order to improve the convergence performance of the holomorphic embedding method, the related technology proposes various improvement schemes, such as flexible holomorphic embedding method, parameterized path holomorphic embedding method and restart holomorphic embedding method. Although the above methods improve the convergence of the holomorphic embedding method, they still have deficiencies in revealing the reasons for the convergence failure of the classical holomorphic embedding method in some power system examples. Therefore, further exploring the convergence mechanism and constructing a better holomorphic embedding form is still a key problem to be solved in this field.

[0109] The existing holomorphic embedding method improves the convergence of the holomorphic embedding method to some extent, but still has deficiencies in revealing the reasons for the failure of convergence of the classical holomorphic embedding method in some power system examples. Among many model parameters and injected data that may affect the convergence of power flow, how to accurately locate the key factors and make targeted adjustments is still a weak link in current research.

[0110] Therefore, the present embodiment takes the failure of convergence of the classical holomorphic embedding method in some complex power grids as a starting point. First, based on the simulation results of the example, a power deviation detection method is introduced to analyze the key factors that cause the classical holomorphic embedding method to fail to converge. Then, the modeling method of the phase-shifting transformer is improved, and the recursive equation and the corresponding solving process of the proposed holomorphic embedding form are derived. The convergence performance of the proposed method is compared with that of the NR and the classical holomorphic embedding. The present embodiment provides a holomorphic embedding method based on improved modeling of the phase-shifting transformer.

[0111] The technical solution adopted by the present embodiment to solve its technical problems is as follows: 1. Power deviation detection method First, the power deviation detection method is introduced to identify the key factors that cause the classical holomorphic embedding method to fail to converge, and further improvement strategies are proposed to improve the convergence of power flow calculation. The specific steps of the power deviation detection method will be described in detail in the case1888rte example. The example system contains 1888 nodes and 2531 lines, with active load of 59111 MW and reactive load of 2271 MVar.

[0112] In the case1888rte system, the power deviation of some nodes (node 422 and node 982) is significantly larger than that of other nodes, with a difference of several orders of magnitude, and shows an approximately symmetric distribution along the horizontal axis.

[0113] Further analysis shows that the voltage amplitude update process of the nodes with large power deviation also shows abnormal behavior with large fluctuation amplitude. Figure 3 The voltage amplitude update of node 422 and node 982 is shown, both of which have severe oscillatory fluctuations with almost identical fluctuation amplitudes, indicating that there is some abnormality between the two nodes. Further observation shows that node 422 and node 982 are connected by a phase-shifting transformer, so it can be suspected that the modeling of the phase-shifting transformer may be the cause of the failure of the power flow calculation to converge. It should be noted that this power deviation and voltage fluctuation anomaly can be observed when using the holomorphic embedding method, but cannot be observed when using the NR method.

[0114] 2. Constructing a power flow calculation model containing an improved phase-shifting transformer Then, the power flow calculation model containing the improved phase-shifting transformer is introduced.

[0115] As shown in Figure 2 , the phase-shifting transformer connecting node i and node n is replaced by an ideal phase-shifting transformer model and a common transmission line jointly proposed by the present embodiment. The model includes an ideal phase-shifting transformer from node i to newly introduced node m, and a common transmission line connecting node m and node n. The ideal phase-shifting transformer model is used to describe the voltage relationship and power transmission relationship between node i and node m. Figure 2 , where Sim represents the complex power flowing from node i to node m, Pim represents the active power flowing from node i to node m, and Qim represents the reactive power flowing from node i to node m.

[0116] On this basis, the following power flow equations are constructed after introducing the ideal phase-shifting transformer.

[0117] Assume an N-node system containing PQ nodes, PV nodes, and a balance node. The specific meanings of the three types of nodes are as follows: PQ node: P and Q are given, and the voltage phase angle and amplitude are to-be-solved variables; PV node: P and voltage amplitude are given, and Q and voltage phase angle are to-be-solved variables; balance node: there is only one balance node, and its voltage amplitude and phase angle are given, and P and Q are to-be-solved variables.

[0118] The corresponding node sets are respectively denoted as , and . If there is a phase-shifting transformer in the system, a new node m is introduced according to the modeling method of Figure 2 . The newly introduced node is regarded as a PQ node, and its injected power is 0, and the voltage is a to-be-solved variable. The newly added node set to which the newly introduced node belongs is denoted as , and the total number of newly added nodes is denoted as NAD. After introducing the new node, the system node set is updated to , and the total number of system nodes is correspondingly expanded to ( ).

[0119] After introducing the new node, the power flow model is adjusted as shown in equations (1)-(4). The power flow equations of the original PQ nodes and PV nodes need to be modified accordingly, and the complex power Sim injected and flowed out by the ideal phase-shifting transformer should be considered in the construction of the power flow model, as shown in equations (1) and (2). The voltage amplitude constraint of the balance node remains unchanged, corresponding to equation (3).

[0120] (1) (2) (3) In the equations: denotes the element in the i-th row and k-th column of the node admittance matrix; is the complex voltage at node k ,in Voltage amplitude, (Voltage phase angle); Inject complex power into node i ( j is the imaginary part unit. To inject active power; (for injecting reactive power). Specify the voltage amplitude for PV nodes or ballast nodes; This indicates the calculation of the conjugate value of a complex number; This indicates the calculation of the real part of a complex number; This indicates the calculation of the absolute value of a complex number. .

[0121] N represents the number of nodes, and the asterisk in the upper right corner represents the deconjugate value; Sim represents the complex power flowing from node i to node m. Equation (1) contains... The value of the sign is determined by the set to which the node belongs: if the node is a newly added node, then... If positive, use a positive sign; otherwise, use a negative sign.

[0122] An ideal phase-shifting transformer constrains the voltage amplitude and phase relationship at its two ends, and the corresponding constraint equation is shown in (4): (4) In the formula: denoted as the set of ideal phase-shifting transformers; im represents the ideal phase-shifting transformer connected between nodes i and m; Vm represents the voltage amplitude at the new node m; τ represents the transformer turns ratio; θshift represents the transformer phase-shifting angle.

[0123] In the revised power flow equations, the changes in the number of variables and equations are as follows: If NAD ideal phase-shifting transformers are added to the system, then 4NAD equations are added accordingly (of which, equations (1) and (4) each increase by 2NAD). Simultaneously, 2NAD complex power variables are introduced. (i.e., NAD each for active and reactive power), and 2NAD node voltage variables (i.e., NAD each for the real and imaginary parts of the voltage). Therefore, the number of new equations is equal to the number of new variables, thus ensuring the solvability of the modified power flow equations in terms of dimensionality.

[0124] 3. Construct a fully embedded form with an improved phase-shifting transformer. The fully embedded form of the power flow equations for PQ nodes, PV nodes, slack nodes, and ideal phase-shifting transformers is constructed as shown in equations (5)-(8).

[0125] (5) (6) (7) (8) where: denotes the embedding of complex variable; denotes the element of the i-th row and the k-th column of the series admittance matrix; denotes the shunt admittance at node i. It is noted that in order to guarantee the holomorphic property of the embedding form, the corresponding embedding form is instead of This is because the former follows the Cauchy-Riemann condition, while the latter does not. and denote the holomorphic functions of the active and reactive power flowing through the ideal phase-shifting transformer, which can be expressed in the form of power series summation as shown in equation (9).

[0126] (9) where: n denotes the order of the power series; s is the complex variable embedding factor, sn denotes the complex variable embedding factor of the n-th order. im denotes the phase-shifting transformer number connected between node i and node m.

[0127] 4. Derivation of the first-order power series (initial solution) The constructed holomorphic embedding form maintains the advantage of the classical holomorphic embedding form in determining the initial solution. The initial solution of each variable is shown in equation (10).

[0128] (10) 5. Derivation of high-order power series (recurrence equation) By extracting the same power series coefficients, the n-th order power series coefficients of the embedding factors on both sides of the equation are equal, and by shifting the high-order power series coefficients to the left and the low-order power series coefficients to the right, the following recurrence equations are obtained as shown in equations (11)-(14).

[0129] (11) (12) (13) (14) where: is the reciprocal term of the complex voltage at node i.

[0130] The recursive equations shown in (11)-(14) are unified so that all the coefficients of the n-th order power series are on the left side of the equation, and all the coefficients of the lower order power series are on the right side of the equation. The unified recursive equation can be expressed as (15): (15) In the formula, A is a recursive matrix required for recursive calculation, which remains constant in the process of recursive calculation; x[n] is the n-th order power series coefficient to be solved; is the right side item of the recursive equation, which is calculated by the coefficients of the lower order power series.

[0131] The effectiveness and accuracy of the proposed full-pure embedding method based on improved phase-shifting transformer modeling are verified, and the CHEM-1, CHEM-2 and NR methods are compared and analyzed. All example analyses are completed on a notebook computer with an Intel Core i9 processor (2.60 GHz) and 32 GB of memory. Programming is realized on the basis of MATPOWER 4.1, and the convergence accuracy of power flow calculation is set to 1x10-6 p.u. and the power base value is 100 MW. CHEM-1 and CHEM-2 are two classical full-pure embedding forms, and the following table lists the embedding form, the processing method of the admittance matrix and other information of each method.

[0132] Figure 4 The following table is a comparison table of the two classical full-pure embedding forms. It should be noted that for the classical full-pure embedding form 1, the admittance matrix is divided into series and parallel parts, and for the classical full-pure embedding form 2, the admittance matrix is divided into symmetric and asymmetric parts.

[0133] Firstly, the accuracy is verified in the modified 9-node system. In the 9-node power system, one power transmission line connected with node 7 and node 8 is replaced by a phase-shifting transformer, and the parameters are set as: resistance r=0.00004 p.u., reactance x=0.0004 p.u., transformation ratio τ=1, and phase-shifting angle θshift from 1° to 5°.

[0134] With the increase of the phase-shifting angle θshift, the convergence performance of the two classical full-pure embedding methods (CHEM-1 and CHEM-2) decreases significantly, and both of them do not converge when the phase-shifting angle θshift=5°. In contrast, the proposed method shows consistent and stable convergence characteristics under different phase-shifting angle scenarios. The proposed method can quickly converge within about 7 recursive calculations, verifying the better and stable convergence performance of the proposed method. With the increase of the phase-shifting angle, the maximum value of the right end item of the admittance matrix under the CHEM-1 and CHEM-2 methods increases significantly, while the maximum value of the right end item of the admittance matrix under the proposed method remains unchanged.

[0135] The comprehensive analysis result can be inferred that the two classical holomorphic embedding methods CHEM-1 and CHEM-2 have defects in dealing with phase-shifting transformers, which leads to the deterioration of the convergence performance of power flow calculation. The reason is that the existence of the phase-shifting angle can significantly increase the numerical value of the right end of the matrix, which is equivalent to connecting a much larger admittance than the actual situation to the node, thereby deviating from the real power grid operating state of the system, and then causing the convergence deterioration. In contrast, the method of the embodiment effectively avoids the above problems by introducing intermediate nodes and using an ideal phase-shifting transformer model, and significantly improves the stability and convergence performance of the calculation.

[0136] Figure 5 The comparison results of the first six order power series coefficients V7[n] and their modulus |V7[n]| at node 7 under the condition of phase-shifting angle θshift=2° are shown for the three methods (CHEM-1, CHEM-2 and the method of the embodiment). As can be seen from the table, with the increase of the order n of the power series, the amplitude of the power series coefficient of the proposed method decreases rapidly, and the 6th order power series coefficient is less than 10-4 p.u. In comparison, the order of the power series coefficients of the CHEM-1 and CHEM-2 methods is greater than that of the proposed method, especially for n=1 and n=2, the amplitude is significantly greater than that of the method of the embodiment. The proposed method achieves faster convergence.

[0137] In addition, the accuracy of the proposed method and the NR method is compared. Under different phase-shifting angles, the comparison results of the voltage amplitude of each node calculated by the proposed method and the NR method are as follows: 1) when θshift=1°, 2°, 3°, the results of the proposed method and the NR method are consistent in the voltage amplitude of each node, almost coinciding, which shows the accuracy of the proposed algorithm; 2) when the phase-shifting angle increases to 3.2°, the NR method has obvious abnormality in the node voltage (the voltage of nodes 4-9 is less than 0.5 p.u.), which shows that the NR algorithm cannot converge, while the proposed method can still converge, which shows that the proposed algorithm has better convergence performance.

[0138] To verify the effectiveness of the proposed method in large-scale systems, the convergence accuracy is set to 1×10-6 p.u. and the maximum number of recursions is set to 30. The embodiment selects 10 typical examples listed in Table 3 for testing. These examples all contain a certain number of phase-shifting transformers, and the number of phase-shifting transformers in each system, the phase-shifting angle of each phase-shifting transformer, and the absolute value of the maximum phase-shifting angle of each phase-shifting transformer are listed in the table. It can be seen that in case1888rte, case1951rte, case6468rte and case_ACTIVSg10k, the absolute value of the maximum phase-shifting angle is large (all more than 9°), while in other examples, the maximum phase-shifting angle is not more than 4°.

[0139] Figure 6 The comparative table of the number of phase-shifting transformers and the size of phase-shifting angles of a plurality of example systems is shown, from which Figure 6 It can be seen that the maximum power deviation of three methods (CHEM-1, CHEM-2 and the method proposed in the embodiment) after reaching the maximum recursion number in 10 test systems. The results show that the proposed method is always superior or comparable to CHEM-1 and CHEM-2 in terms of power deviation, showing better convergence performance. Especially in systems with large phase-shifting angles, such as case1888rte, case1951rte, case6468rte and case_CTIVSg10k test systems, the maximum power deviation of the proposed algorithm is much smaller than that of CHEM-1 and CHEM-2, indicating the significant advantage of the proposed method, further proving its effectiveness and reliability in complex power systems.

[0140] In addition, the convergence and computational efficiency of the proposed method and the NR method are compared. The NR method uses flat start and non-flat start (the results of the fast decomposition method are iterated twice as the initial value) for power flow calculation. Table 4 shows the calculation time and the number of iterations (recursions) required for convergence of each example.

[0141] In the case_ACTIVSg10k system, the NR method cannot converge under flat start conditions, while the proposed method can converge smoothly, fully embodying the superior convergence characteristics of the proposed method. In addition, in terms of calculation time, in the case1354pegase and case_ACTIVSg10k systems, the proposed method also shows a significant speed advantage compared to the non-flat start NR method. Comprehensive analysis further verifies the application potential and engineering value of the proposed method in complex power system power flow analysis.

[0142] Figure 7 The table showing the comparison of computational efficiency and convergence of the proposed method and the NR method is shown.

[0143] The present embodiment takes the convergence failure of the classic holomorphic embedding method in some complex power grids as the starting point, introduces a power deviation detection method according to the simulation results, and analyzes the key factors that cause the classic holomorphic embedding method to fail to converge.

[0144] The present embodiment proposes an improved power flow calculation model of phase-shifting transformers, which uses an ideal phase-shifting transformer combined with a conventional transmission line modeling method to replace the traditional phase-shifting transformer model.

[0145] The present embodiment proposes that the solution of the nonlinear equation set is non-iterative, with low dependence on initial values, and can guarantee convergence when there is a solution, and can send a signal when there is no solution.

[0146] The embodiment deduces the recursive equation of the proposed holomorphic embedding form and the corresponding solving process, and compares the convergence performance of the proposed method and the NR and the classical holomorphic embedding. The convergence of the proposed method in the power flow calculation is better than that of the classical holomorphic embedding method, and the proposed method shows good adaptability and engineering application potential.

[0147] The embodiment has higher reliability and lower dependence on initial value selection, and can send a signal when the equation has no solution. The embodiment introduces a power deviation detection method to identify the key factors leading to the non-convergence of the classical holomorphic embedding method. The embodiment adopts an ideal phase-shifting transformer combined with a conventional transmission line modeling method to replace the traditional phase-shifting transformer model, and the holomorphic embedding form constructed accordingly shows good convergence performance.

[0148] According to an embodiment of the present application, an electronic device is provided. The electronic device in the embodiment can include one or more of the following components: a processor, a network interface, a memory, a non-volatile memory, and one or more application programs, wherein the one or more application programs can be stored in the non-volatile memory and configured to be executed by the one or more processors, and the one or more programs are configured to perform the method as described in the foregoing method embodiments.

[0149] According to an embodiment of the present application, a computer readable storage medium is provided, which stores a computer program, and the computer program is executed by a computer to make the computer perform the method described in any of the foregoing embodiments.

[0150] According to an embodiment of the present application, a computer program product containing instructions is also provided, and the instructions are executed by a computer to make the computer perform a method in any of the foregoing embodiments.

[0151] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application and the above-described drawings are used to distinguish similar objects, and do not necessarily indicate a specific order or sequence. It should be understood that the data thus used can be interchanged under appropriate circumstances, so that the embodiments of the present application described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device including a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but can include other steps or units not clearly listed or inherent to the process, method, product or device.

[0152] Optionally, specific examples in the embodiments can refer to the examples described in the foregoing embodiments, and the embodiments will not be described here again.

[0153] The above-mentioned sequence numbers of the embodiments of the present application are only for description, and do not represent advantages or disadvantages of the embodiments.

[0154] In the above-mentioned embodiments of the present application, the description of each embodiment has its own focus, and the parts not described in detail in a certain embodiment can be referred to the relevant description of other embodiments.

[0155] The above-mentioned only is the preferred embodiment of the present application, it should be pointed out, for the ordinary skilled person in the art, without departing from the principle of the present application, can make a number of improvements and refinements, these improvements and refinements should also be considered as the protection scope of the present application.

Claims

1. A method of modeling an electric power system, characterized by, include: Identify the target factors that cause the holomorphic embedding method to fail to converge; Based on the aforementioned target factors, the phase-shifting transformers carried in the target power system are decomposed into a combination of ideal phase-shifting transformers and ordinary transmission lines, and new nodes are introduced as AD nodes to construct a power model; wherein, the AD node is a power node with injected power that is always zero. Based on the power model, the power flow model is reconstructed to obtain the reconstructed power flow model; wherein, the reconstructed power flow model includes the complex power balance equations of PQ nodes and AD nodes, the active power balance equations and voltage amplitude constraint equations of PV nodes, the voltage amplitude constraint equations of the slack nodes, and the phase-shift constraint equations of the ideal phase-shifting transformer.

2. The modeling method of claim 1, wherein, The step of determining the target factors that cause the holomorphic embedding method to fail to converge includes: A power deviation-based detection method is used to identify the target factors that cause the fully embedded method to fail to converge; wherein, the target factors include numerical instability caused when the phase shift angle of the phase-shifting transformer exceeds a first threshold.

3. The modeling method of claim 2, wherein, The step of determining the target factors causing the fully pure embedding method to fail to converge using a power deviation-based detection method includes: Perform power flow calculations using the fully embedded method on the target power system, record the voltage update value of each node during the power series recursion process, and calculate the voltage oscillation amplitude. Calculate the power deviation value for each node; wherein the power deviation value is the difference between the actual injected power and the theoretical power flow power of the node; If a pair of nodes simultaneously meets the following conditions, it is determined to be an abnormal node connected to the phase-shifting transformer: the power deviation value exceeds the second threshold, the voltage oscillation amplitude exceeds the third threshold, and the fluctuation trend is synchronized. The pair of nodes is determined to be connected by a phase-shifting transformer, and the phase shift angle of the phase-shifting transformer exceeding a first threshold is taken as the target factor.

4. The modeling method of claim 1, wherein, The complex power balance equations for the PQ node and the AD node are expressed as follows: In the formula, represents the total number of nodes in the system, represents the element in the i-th row and the k-th column of the node admittance matrix, is the complex voltage at node k, is the complex power injected at node i, is the complex power flowing from node i to node m, and im represents an ideal phase-shifting transformer connected between nodes i and m, represents a set of ideal phase-shifting transformers, represents a set of PQ nodes, represents a set of AD nodes, represents the conjugate value of a complex number, and N represents the number of nodes, represents the conjugate value of the complex voltage at node i, ; The active power balance equation and voltage amplitude constraint equation of the PV node are expressed as follows: in the formula, denotes the conjugate value of the complex voltage at node i, denotes the element of the node admittance matrix in the i-th row and k-th column, is the complex voltage at node k, denotes the injected active power at PV node i, denotes the sum of the active power of all ideal phase-shifting transformers connected to node i, denotes the real active power consumed by the ideal phase-shifting transformer itself, denotes the specified voltage magnitude at PV node or slack node, denotes the set of PV nodes, denotes the real part of the complex number; denotes the absolute value of the complex number.

5. The modeling method of claim 4, wherein, The voltage magnitude constraint equation for the balancing node is expressed as: In the formula, is represented as a set of balanced nodes; The phase-shifting constraint equation of the ideal phase-shifting transformer is expressed as: where, denotes the set of ideal phase-shifting transformers, denotes an ideal phase-shifting transformer connected between nodes i and m; denotes the voltage amplitude at the new node m, denotes the transformer ratio, and θshift denotes the transformer phase-shift angle.

6. A method of calculating a power flow model of an electric power system, characterized by, include: For the reconstructed power flow model, complex variables are embedded and a power flow model in a fully embedded form is constructed; wherein, the reconstructed power flow model is the reconstructed power flow model as described in any one of claims 1-5; The fully embedded power flow model is solved using a preset solution algorithm until the convergence accuracy is met, and the result parameters of each node in the target power system are obtained.

7. The computational method of claim 6, wherein, The fully embedded power flow model includes: complex power balance equations for PQ and AD nodes in the fully embedded form, active power balance equations and voltage amplitude constraint equations for PV nodes in the fully embedded form, voltage amplitude constraint equations for slack nodes in the fully embedded form, phase-shift constraint equations for the ideal phase-shifting transformer in the fully embedded form, and fully embedded functions of active and reactive power flowing through the ideal phase-shifting transformer.

8. The computational method of claim 7, wherein, The complex power balance equations for the PQ node and AD node in the pure embedded form are expressed as follows: In the formula, ; The active power balance equation and voltage amplitude constraint equation for a purely embedded PV node are expressed as follows: In the formula, ; The voltage magnitude constraint equation for a purely embedded balancing node is expressed as: The phase-shifting constraint equation for the ideal phase-shifting transformer in its pure embedded form is expressed as: In the formula, ; The holomorphic functions of active and reactive power flowing through an ideal phase-shifting transformer are expressed as: in the formula, denotes the complex variable embedded as, denotes the element of the series admittance matrix in the ith row and the kth column; denotes the parallel admittance at node i, denotes the holomorphic function of the complex voltage at node k, denotes the conjugate of the complex power injected at node i, denotes the holomorphic function of the active power flowing through the ideal phase-shifting transformer, denotes the holomorphic function of the reactive power flowing through the ideal phase-shifting transformer, denotes the parallel admittance at node i, denotes the holomorphic function of the complex voltage at node i, denotes the set of PQ nodes, denotes the set of AD nodes, denotes the holomorphic function of the complex voltage conjugate at node i, denotes the injected active power at PV node i, is the imaginary unit, is the holomorphic function of the reactive power at PV node i, is the set of PV nodes, n denotes the order of the power series; s is the complex variable embedding factor, sn denotes the complex variable embedding factor of the nth order.

9. The computational method of claim 8, wherein, The step of solving the fully embedded power flow model using a preset solution algorithm until the convergence accuracy is met, and obtaining the result parameters of each node in the target power system, includes: For the fully embedded power flow model, a corresponding recursive equation is constructed; wherein, the recursive equation establishes a recursive relationship between the parameters to be solved by extracting the relationship between the coefficients of higher-order power series and the coefficients of lower-order power series. For the recursive equation, recursive calculations are performed to obtain the result parameters for each node in the target power system; wherein, the recursive equation includes: The recursive equations for nodes PQ and AD are expressed as follows: In the formula, Let this be the current recursion order. For the nth power series coefficients of the voltage at node k, ... These are the coefficients of the nth power series of active power losses in a phase-shifting transformer. The coefficients of the nth power series of reactive power loss in a phase-shifting transformer are given. Let Vi be the conjugate of the reciprocal of the complex voltage Vi at node i. The reciprocal of the voltage at node i The Conjugate of order coefficients, The lower-order recursion sequence number. This means that nodes with AD are positive and nodes without AD are negative. The recurrence equations for PV nodes and equilibrium nodes are expressed as follows: In the formula, Represented as the Kronecker delta function, Let the coefficients of the nth power series of reactive power at PV node i be represented. ; The recursive equation for a phase-shifting transformer is expressed as follows: In the formula, This represents the nth-order coefficient of the voltage at primary node i of the phase-shifting transformer. This represents the nth-order coefficient of the voltage at the newly added node m of the phase-shifting transformer. ; The unified recursive equation is expressed as: In the formula, A is the recursive matrix required for recursive calculation, which remains constant during the recursive calculation process; x[n] is the coefficient of the nth power series to be calculated. This is the right-hand side term of the recursive equation, which is calculated from the coefficients of a power series of order less than n.

10. An electronic device, characterized in that, include: A memory, and one or more processors communicatively connected to the memory; The memory stores instructions that can be executed by the one or more processors to cause the one or more processors to implement the method as described in any one of claims 1 to 9.

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