All-pure embedded power flow algorithm based on power restart

Abstract

The application proposes a full-pure embedded power flow algorithm based on power restart, constructs a PRHEM power flow model and introduces a power restart mechanism; takes a classic HEM algorithm as an initial start model, calculates a maximum power residual error AS of the model step by step, judges whether the model needs to be restarted according to a convergence rate change condition; if the model does not need to be restarted, directly outputs a power flow convergence result; if the model needs to be restarted, obtains a numerical solution of a voltage analytic function and a corresponding power state as an initial state, updates the PRHEM power flow model by restarting and continues to calculate power series coefficients and the maximum power residual error; constantly updates the initial state of the model, shortens a spatial distance between the initial state power and the target state power, until the PRHEM power flow model converges, and outputs an analytic solution obtained by the converged model; the application limits recursive solving calculation in low orders, avoids convergence problems caused by high-order power series calculation, and guarantees stable convergence of power flow calculation under large-scale power grids and heavy load conditions.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power system power flow calculation, and in particular to a holomorphic embedding power flow algorithm based on power restart. BACKGROUND

[0002] Power flow calculation is the basis of power system operation and planning. The current common power flow calculation methods are mainly based on the principle of numerical iteration, such as Newton-Raphson method (NRM), fast decoupled method, etc. However, with the large investment of control devices and renewable energy in new power systems, the traditional power flow calculation method is increasingly difficult to cope with the flexible and variable power system operation scenarios, the dependence on initial value of the algorithm is stronger, and the convergence is worse. Holomorphic embedding method (HEM) has the advantages of not depending on initial value selection, being able to reliably converge to the system operable solution and obtaining an analytical solution, and is widely used in power flow analysis of new power systems. However, in the actual large power grid and heavy load power flow calculation, the order of power series required by the classical HEM algorithm is high, and the convergence is poor.

[0003] Studies have shown that when performing power flow calculation on actual large-scale, heavy-load systems, the classical HEM power flow algorithm requires high-order power series calculation, and there are problems of unstable convergence. When the algorithm performs high-order power series coefficient calculation, numerical instability is prone to occur, and the method may converge slowly or even not converge.

[0004] In view of such problems, Chiang H D, Wang T, etc. proposed a fast and flexible HEM power flow algorithm, which allows flexible configuration of its voltage initial solution to reduce the order of solution and shorten the solution time, but sacrifices the initial value insensitivity of the HEM power flow algorithm. When the initial value prediction is unreasonable, the convergence may deteriorate. Li Xue, Yao Chaofan, etc. proposed a HEM power flow algorithm with dynamic updating of constant term value, which reduces the order of power series required for power flow convergence and improves the convergence performance and calculation efficiency of the algorithm. Freitas FD, Jr A S, etc. use power restart calculation strategy to update the voltage state, thereby shortening the time-consuming of HEM solving power system power flow calculation. However, the restart methods of the above methods are heuristic and lack strict physical basis, and the convergence effect under different working conditions cannot be guaranteed, and the application scene is limited. SUMMARY

[0005] The present application aims to propose a holomorphic embedding power flow algorithm based on power restart, which limits recursive solution calculation to low order, avoids the convergence problem caused by high-order power series calculation, and ensures stable convergence of power flow calculation in large-scale power grids and heavy load conditions.

[0006] To achieve the above object, the technical scheme of the present application is: a power restart holomorphic embedded power flow algorithm (PRHEM) is constructed, a PRHEM power flow model is built, and a power restart mechanism is introduced; a classical HEM algorithm is taken as an initial starting model, the maximum power residual ΔS of the model is calculated step by step, and according to the convergence rate change, it is judged whether the model needs to be restarted; if not, the power flow convergence result is directly output; if yes, the numerical solution of the voltage analytic function and the corresponding power state are solved, which are taken as the initial state to update the PRHEM power flow model, and the power series coefficient and the maximum power residual are continued to be calculated step by step; according to the power restart mechanism, the initial state of the model is continuously updated, the spatial distance between the initial state power and the target state power is shortened, until the PRHEM power flow model converges, and the analytic solution obtained by the converged model is output.

[0007] Further, the PRHEM power flow model is constructed as follows:

[0008] The to-be-solved quantity x of the nonlinear power flow equation f(x)=0 is constructed as a holomorphic function, and is embedded into the nonlinear power flow equation to obtain a holomorphic embedded power flow equation f(x)=f[x(s)]=0, wherein the to-be-solved quantity x includes node voltage and generator reactive power, x(s) is a holomorphic function on the complex domain U, which is expanded into a power series form in the complex domain as formula (1):

[0009]

[0010] In the formula, x[n] is the power series coefficient of the holomorphic function; s is the embedding factor of the holomorphic embedded model.

[0011] Based on the flexible HEM power flow algorithm, the initial state power and the direction correction power are defined in the power injection space;

[0012]

[0013] In the formula, the subscripts i and k represent node numbers; N represents the total number of nodes; is the conjugate form of the element of the i-th row and the k-th column of the node admittance matrix; S i is the complex power of the PQ node i, S i0 is the initial state power of the PQ node i, S id is the direction correction power of the PQ node i; P i is the active power of the PV node i, P i0 is the initial state power of the PV node i, P id is the direction correction power of the PV node i, Qi [0] is the initial reactive power of PV node i; V i0 represents the initial value of voltage of node i, represents the conjugate of V i0 represents the initial value of voltage of node i, i0 represents the initial value of voltage of node i, represents the initial value of voltage of node k V k0 represents the conjugate form of V

[0014] The balanced node model is as follows:

[0015]

[0016] In the formula, represents the given value of voltage of node i; V i (s) is the analytic function of voltage of node i.

[0017] The HEM power flow equation is reconstructed by formula (1) and (2), and the PRHEM model of PQ node in the power injection space is obtained as follows:

[0018]

[0019] In the formula, V k (s) is the analytic function of voltage of node k.

[0020] The holomorphic embedding form of the conjugate form of all node voltage analytic functions V(s) satisfies the following conditions:

[0021]

[0022] In the formula, is the conjugate form of V[n]

[0023] The PRHEM model of the PV node is constructed as follows:

[0024]

[0025] In the formula, represents the given value of voltage of node i, represents the given amplitude of voltage of node i, Q i (s) is the holomorphic analytic function of reactive power of PV node i, and j represents an imaginary number,

[0026] Further, the maximum power residual ΔS of the step-by-step calculation model is used to judge whether the model is restarted according to the convergence rate change, and specifically:

[0027] a. Set the convergence precision ε;

[0028] b. Solve the n-th order power series coefficient of the voltage analytical function, and calculate the numerical solution of the voltage analytical function at s = 1, and calculate the maximum power residual value ΔS of the n-th order power series coefficient n ;

[0029] c. Determine whether ΔS n is less than ε, if ΔS n < ε, the PRHEM power flow model is not restarted, and the power flow convergence result is directly output (the first start is the classic HEM model, and the subsequent is the PRHEM model); if ΔS n ≥ ε, determine whether n is less than 2;

[0030] d. If n < 2, let n = n + 1 and return to step b; if n ≥ 2, determine whether ΔS n satisfies the following relationship:

[0031]

[0032] If yes, the numerical solution of the voltage analytical function at s = 1 and the corresponding power state are taken as the initial state to restart the PRHEM power flow model, and n = n + 1 is taken, and then step b is returned; if no, n = n + 1 is taken, and then step b is returned.

[0033]

[0034] Further, the initial state of the updated model is specifically:

[0035] The numerical solution obtained by the model (the classic HEM model for the first start, and the PRHEM model for the subsequent restart update) at s = 1 is taken as the voltage initial solution of the PRHEM power flow model after the restart update, and the power obtained by calculating the updated voltage initial value by formula (2) is taken as the initial state power of the PRHEM power flow model after the restart update, so as to realize the restart update of the PRHEM power flow model.

[0036] Further, the PRHEM power flow model is specifically solved as follows:

[0037] The restarted PRHEM power flow model obtains the recursive calculation matrix equation of each node model according to the power series coefficient equivalence principle,

[0038] The balanced node

[0039]

[0040] In the formula, Re(·) is a real part function; Im(·) is an imaginary part function; V i [n] is the n-th order coefficient of the voltage analytical function V i (s), and the superscripts Re and Im represent the corresponding real part and imaginary part; δ​n0 with δ n1 is a pulse function, which means that the function value is 1 if and only if the subscript n = 0 or n = 1.

[0041] PQ node

[0042]

[0043] where the variable parameters in the brackets represent the corresponding order of the coefficients; G i,k , B i,k are the real and imaginary parts of Y i,k , which represent the conductance and susceptance relationship between node i and node k; the expression of auxiliary variable K[n-1] is as follows:

[0044]

[0045] where the variable parameters in the brackets represent the corresponding order of the coefficients; W i [·] is the power series coefficient W i (s) of the auxiliary holomorphic function; W i (s) is the reciprocal form of V i (s), which helps to perform Taylor expansion on the equation in the model with denominator V i (s);

[0046]

[0047] PV node

[0048]

[0049] where Q i [n] is the n-th order coefficient of PV node reactive analytic function Q i (s); the superscripts Re and Im represent the real and imaginary parts of the variable, respectively; the expressions of auxiliary variables L[n-1], D[0] and M[n-1] are as follows:

[0050]

[0051] The recursive matrix equation for constructing the power flow model is established, and based on the matrix transformation technique, the following matrix equation can be obtained by combining equations (8), (9) and (12):

[0052]

[0053] where the subscripts VS, PQ and PV represent the numbers of the three types of nodes, i.e. balance, PQ and PV, which correspond to the node numbers i and k mentioned above; the auxiliary variables and can be expressed as:

[0054]

[0055] By means of equation transformation and equation replacement, Q PV [n] is moved to the left side of the equation, and is replaced by in accordance with equation (12) to express the equation, so that all unknown variables are on the left side of the equation and all known quantities are on the right side of the equation; the following equation is obtained:

[0056]

[0057] The recursive matrix equation calculation form of the final power flow model can be expressed as:

[0058] AX = b (17)

[0059] In the equation, A is a linear equation coefficient matrix generated in the recursive calculation process; X is a model to-be-solved power series coefficient vector; and b is a known vector calculated by not more than n-1 order coefficients.

[0060] Compared with the prior art, the present application has the following beneficial effects:

[0061] 1) The present application updates the model power state by the initial state power, improves the analytic continuation direction of the model by the direction correction power, avoids the problem of numerical instability in the voltage and reactive power analytic function approximation process, effectively deals with the poor convergence condition in the actual large power grid and heavy load power flow calculation, and improves the adaptability of the holomorphic embedding power flow algorithm.

[0062] 2) The present application proposes an update criterion of the restart mechanism based on the change condition of the maximum power residual, and compared with the way of setting a fixed upper limit of the power series order to restart the model, the proposed restart way has a more explicit physical meaning, higher calculation efficiency and more stable convergence performance.

[0063] 3) The present application corrects the approximation direction of the voltage and reactive power analytic function by the power restart way, guarantees that the power flow solution is finally located in the convergence domain, the numerical solution under the target state can be obtained by directly summing the power series, and the calculation cost of the algorithm is lower. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 The present application is a PRHEM power flow algorithm calculation flowchart;

[0065] Figure 2 The present application is a HEM power flow algorithm maximum power residual ΔS convergence change diagram. DETAILED DESCRIPTION

[0066] The technical solutions of the present application will be specifically described below with reference to the accompanying drawings. Figures 1-2 The technical solutions of the present application will be specifically described below with reference to the accompanying drawings.

[0067] The application proposes a power restart holomorphic embedded power flow algorithm (PRHEM) based on power restart, constructs a PRHEM power flow model and introduces a power restart mechanism; the existing classical HEM algorithm is taken as an initial start model, the maximum power residual ΔS of the model is calculated step by step, and according to the convergence rate change, it is judged whether the model needs to be restarted; if not, the power flow convergence result is directly output; if it needs to be restarted, the numerical solution of the voltage analytic function and the corresponding power state are obtained, which are taken as the initial state to update the PRHEM power flow model, and the power series coefficient and the maximum power residual are continued to be calculated step by step; according to the power restart mechanism, the initial state of the model is constantly updated, the spatial distance between the initial state power and the target state power is shortened, until the PRHEM power flow model converges, and the analytic solution obtained by the converged model is output.

[0068] In this embodiment, the PRHEM power flow model is constructed as follows:

[0069] According to the definition of holomorphic function, when the complex function x(s) satisfies the Cauchy-Riemann equation and is differentiable in a neighborhood U of a point, the function x(s) is called a holomorphic function on the complex domain U, which is expanded into a power series in the form of formula (1).

[0070]

[0071] In the formula, x[n] is the power series coefficient of the holomorphic function; s is the embedding factor of the holomorphic embedded model.

[0072] For the nonlinear power flow equation f(x) = 0 which is difficult to solve, the to-be-solved quantity x (including node voltage and generator reactive power) is constructed as a holomorphic function in the form of formula (1), and is embedded into the nonlinear power flow equation to obtain a holomorphic embedded power flow equation f(x) = f[x(s)] = 0. According to the principle that the power series coefficients on both sides of the equation are equal, the recursive relationship of the equation is derived, each order coefficient x[n] is obtained, and the analytic expression of the to-be-solved quantity x is obtained.

[0073] When the power flow equation is holomorphic embedded, the following four basic conditions need to be ensured:

[0074] 1) In f[x(s)] = 0, the function x(s) has holomorphicity;

[0075] 2) For the holomorphic embedded power flow equation f[x(s)] = 0, when s = 0, the solution x(0) of the equation has actual physical meaning and is easy to obtain;

[0076] 3) For holomorphic embedding power flow equation f[x(s)] = 0, when s = 1, f[x(1)] is completely equivalent to the original nonlinear power flow equation f(x), and x(1) is the target solution of f(x) = 0;

[0077] 4) On the s path before reaching the saddle node bifurcation point, f[x(s)] = 0 does not have an additional saddle node bifurcation point, that is, f[x(s)] is continuous in the analytical continuation process of s from 0 to 1 and is not interrupted by a saddle node bifurcation point.

[0078] In view of the flexible HEM power flow algorithm which can flexibly configure the initial solution, the present application defines the initial power state and the target power state based on the power injection space, so as to represent the physical space relationship between the initial solution and the target solution, and uses the direction correction power to represent the analytical continuation direction of the HEM; and the initial state power and the direction correction power are flexibly updated by using the restart mechanism, so that the initial state power continuously approaches the target state power, and the reliable convergence of the power flow is ensured.

[0079] The model is based on the flexible HEM power flow algorithm, and defines the initial state power and the direction correction power in the power injection space.

[0080]

[0081] In the formula, the subscripts i and k represent node numbers; N represents the total number of nodes; is the conjugate form of the element of the node admittance matrix in the i-th row and the k-th column; S i is the complex power of the PQ node i, S i0 is the initial state power of the PQ node i, S id is the direction correction power of the PQ node i; P i is the active power of the PV node i, P i0 is the initial state power of the PV node i, P id is the direction correction power of the PV node i, Q i [0] is the reactive power of the PV node i in the initial state; V i0 represents the voltage initial value of the node i, represents the voltage initial value V k0 of the node k.

[0082] The HEM power flow equation is reconstructed by formula (1) and (2), and the PRHEM model of the PQ node in the power injection space is obtained as follows:

[0083]

[0084] In the formula, V k (s) is the voltage analytical function of the node k.

[0085] Since the holomorphic embedding of the power flow equation needs to satisfy the Cauchy-Riemann condition, the holomorphic embedding of the conjugate form of V(s) satisfies the following condition:

[0086]

[0087] where, is the conjugate form of V[n].

[0088] In addition, in order to better consider the analytical relationship between the node voltage amplitude and the generator reactive power, the PRHEM model of the PV node is constructed as follows:

[0089]

[0090] where, represents the given value of the voltage of node i, represents the given amplitude of the voltage of node i, and j represents an imaginary number,

[0091] The construction of the model retains the holomorphic analytical function Q(s) of the reactive power of the PV node, so as to directly analyze the change of the reactive state of the node through the reactive analytical function, and provide a basis for the switching of the reactive device of the node. If equation transformation and conjugate symmetry processing are performed on equation (5), the equation can be equivalent to the flexible HEM power flow equation.

[0092] The balanced node model is as follows:

[0093]

[0094] As can be seen from equations (2) to (6), the power flow model of the algorithm is essentially consistent with the flexible HEM power flow algorithm when the restart is not performed, and has the advantage of flexible start from any state, which provides a basic condition for the use of the restart mechanism.

[0095] In this embodiment, the power restart mechanism is as follows:

[0096] On the basis of the above model, the restart mechanism is introduced, the position of the initial state power is constantly updated in the power injection space, the distance between the initial state power and the target state power is shortened, the direction of the analytic continuation of the voltage and reactive power analytic function is corrected, and the stable convergence of the system power flow model is physically ensured. When the model performs recursive operation, the voltage analytic function obtained is solved for numerical solution after each higher order power series coefficient is calculated, and the maximum power residual AS of the model is calculated using the numerical solution. The trend of AS reflects the change of the holomorphic embedding model in the power injection space during the analytic continuation to some extent, and can be used as a criterion for whether to continue the recursive calculation or whether to restart the power. At the same time, AS is also the basis for judging whether the power flow converges. Therefore, the restart mechanism is combined with the HEM power flow algorithm from the perspective of the power injection space, which has good adaptability in theory.

[0097] The most important thing for the HEM power flow algorithm is to ensure that the updated initial state has practical physical meaning, so the first thing to determine is the initial starting point of the model. In order to easily obtain the initial state power of the model, the classical HEM power flow algorithm is used as the starting model. When the system size is small or the load is light, the power series order required for the convergence of the classical HEM power flow algorithm is low, and the algorithm does not need to be restarted, and the convergence result is directly output; when the system size is large or the load is heavy, the convergence speed change rate of the algorithm is calculated to determine whether to restart and update the model.

[0098] Since the maximum power residual AS of the HEM power flow algorithm decreases continuously with the increase of the power series order, as shown in Figure 2 It can be seen that the decreasing amount of AS decreases continuously in the convergence process of the algorithm. Therefore, in the setting of the restart mechanism, the algorithm combines the set convergence precision ε, and takes the convergence speed change of the numerical solution of AS obtained after each recursive calculation as the judgment basis. When restart is needed, the numerical solution of the voltage analytic function obtained at s=1 by the model (the classical HEM model for the first start, and the PRHEM model for the subsequent restart update) is taken as the voltage initial solution of the model after restart update, and the power obtained by calculating the updated voltage initial value by formula (2) is taken as the initial state power of the model after restart update, so as to realize the restart update of the model.

[0099] The specific process is as follows:

[0100] e. Set the convergence precision ε;

[0101] f. Solve the nth order power series coefficient of the voltage analytic function, calculate the numerical solution of the voltage analytic function at s=1, and calculate the maximum power residual value AS n ;

[0102] g. Judge ASn whether less than ε, if ΔS n <ε, no need to restart, directly output the power flow convergence results (the first start to output the results of the classic HEM model, and the subsequent PRHEM model output results); if ΔS n ≥ε, judge whether n is less than 2;

[0103] h. If n<2, let n=n+1 and return to step b; if n≥2, judge whether ΔS n whether to meet the following relationship:

[0104]

[0105] If yes, the numerical solution of the obtained voltage analytic function at s=1 and its corresponding power state are taken as the initial state to restart the PRHEM power flow model, and let n=n+1 and return to step b;

[0106] If no, let n=n+1 and return to step b.

[0107] From the power injection space, the setting of the restart mechanism takes the rate of the initial state power approaching the target state power as the criterion, which has clear physical meaning. At the same time, the restart mechanism limits the algorithm to low-order power series calculation, avoiding the numerical stability problem in high-order power series calculation, reducing the convergence oscillation or stagnation solution phenomenon caused by high-order power series calculation. Moreover, the numerical solution at the target state can be obtained by direct summation, without the need for Padé approximation calculation, reducing the algorithm calculation cost.

[0108] In this embodiment, the PRHEM power flow model is solved as follows:

[0109] The restart model can obtain the recursive calculation matrix equation of each node model according to the power series coefficient equivalence principle:

[0110] 1) Balanced node

[0111]

[0112] In the formula, Re(·) is the real part function; Im(·) is the imaginary part function; V i [n] is the n-order coefficient of the voltage analytic function V i (s), and the superscripts Re and Im represent the corresponding real part and imaginary part; δ n0 and δ n1 are impulse functions, which represent that the function value is 1 only when the subscript n=0 and n=1.

[0113] 2) PQ node

[0114]

[0115] where G i,k and B i,k are the real and imaginary parts of Y i,k , representing the conductance and susceptance relationship between node i and node k; the auxiliary variable K[n-1] is expressed as follows:

[0116]

[0117] where the variable parameters in [] represent the corresponding order of coefficients; W i [·] is the power series coefficient of the auxiliary holomorphic function W i (s), W i (s) is the reciprocal form of V i (s), helping to perform Taylor expansion on the equation in the model with denominator V i (s).

[0118]

[0119] 3) PV node

[0120]

[0121] where Q i [n] is the n-th order coefficient of the PV node reactive analytic function Q i (s); the superscripts Re and Im represent the real and imaginary parts of the variable, respectively; the auxiliary variables L[n-1], D[0] and M[n-1] are expressed as follows:

[0122]

[0123] 4) Recursive matrix equation for constructing the power flow model

[0124] Meanwhile, by combining equations (8), (9) and (12), based on matrix transformation techniques, the following matrix equation can be obtained:

[0125]

[0126] where the subscripts VS, PQ and PV represent the numbers of the three types of nodes, i.e. balance, PQ and PV, corresponding to the node numbers i and k mentioned above; the auxiliary variables and can be expressed as:

[0127]

[0128] By using the method of equation transformation and equation replacement, the Q PV [n] on the right side of equation (14) is moved to the left side, and is replaced by The expression is made, so that the unknown variables of the equation are all on the left side of the equation, and the known quantities are all on the right side of the equation. The following formula is obtained:

[0129]

[0130] The recursive matrix equation calculation form of the final power flow model can be expressed as:

[0131] AX = b (17)

[0132] In the formula, A is a linear equation coefficient matrix generated in the recursive calculation process; X is a model to-be-solved power series coefficient vector; and b is a known vector calculated by not more than n-1 order coefficients.

[0133] The above is the preferred embodiment of the present application. Any change made according to the technical solution of the present application, as long as the function generated does not exceed the scope of the technical solution of the present application, belongs to the protection scope of the present application.

Claims

1. A full-pure embedded power flow algorithm based on power restart, characterized in that, The PRHEM power flow model is constructed and a power restart mechanism is introduced; a classical HEM algorithm is used as an initial starting model, the maximum power residual ΔS of the model is calculated step by step, and whether the model needs to be restarted is judged according to the convergence rate change; if the power restart is not needed, the power flow convergence result is directly output; if the power restart is needed, the numerical solution of the voltage analytical function and the corresponding power state are obtained, which are used as the initial state to update and restart the PRHEM power flow model, and the power series coefficient and the maximum power residual are continuously calculated step by step, according to the power restart mechanism, the initial state of the model is continuously updated, the spatial distance between the initial state power and the target state power is shortened, until the PRHEM power flow model converges, and the analytical solution obtained by the converged model is output; The PRHEM power flow model is constructed as follows: The to-be-solved quantity x of the nonlinear power flow equation f(x) = 0 is constructed as a holomorphic function, and the holomorphic function is embedded into the nonlinear power flow equation to obtain a holomorphic embedded power flow equation f(x) = f[x(s)] = 0, wherein the to-be-solved quantity x includes node voltage and generator reactive power, x(s) is a holomorphic function on the complex domain U, and the holomorphic function is expanded into a power series form as formula (1): In the formula, x[n] is a power series coefficient of the holomorphic function; s is an embedding factor of the holomorphic embedded model; Based on the flexible HEM power flow algorithm, the initial state power and the direction correction power are defined in the power injection space; where subscript i and k represent node number; N represents total node number; is the conjugate form of the element in the i-th row and k-th column of the node admittance matrix; S i is the complex power of PQ node i, S i0 is the initial state power of PQ node i, S id is the direction correction power of PQ node i; P i is the active power of PV node i, P i0 is the initial state power of PV node i, P id is the direction correction power of PV node i, Q i [0] is the reactive power of PV node i in the initial state; V i0 represents the voltage initial value of node i, represents the voltage initial value V k0 of node k; and is the conjugate form of The balanced node model is as follows: wherein V represents the voltage given value of the node i; i (s) is the voltage analytical function of the node i; The PRHEM model of the PQ node in the power injection space is obtained by reconstructing the HEM power flow equation through formula (1) and (2) as follows: wherein V k (s) is the voltage analytical function of node k; The conjugate form of all the nodal voltage analytic functions V(s) satisfies the following conditions: wherein is the conjugate of V[n] The PRHEM model of the PV node is constructed as follows: wherein represents the amplitude of the voltage given value of the node i, Q i (s) is a holomorphic function of the form of the reactive power of the PV node i, j represents imaginary number, 2. The power swing based full-purely embedded power flow algorithm of claim 1, wherein, The maximum power residual ΔS of the model is calculated step by step, and whether the model needs to be restarted is judged according to the convergence rate change, and the specific steps are as follows: a. Set the convergence precision ε; b. Solving the nth order power series coefficient of the voltage analytical function and calculating the numerical solution of the voltage analytical function at s = 1, and calculating the maximum power residual value AS to the nth order power series coefficient n ; c. judge whether ΔS n is less than ε, if ΔS n is less than ε, the power flow convergence result can be output directly without restarting, the first starting output result is the classical HEM model, and the subsequent output result is the PRHEM model; if ΔS n is greater than or equal to ε, it is judged whether n is less than 2; d.If n < 2, then let n = n + 1 and return to step b; if n > 2, then determine whether ΔS n satisfies the following relationship: If the condition is met, the numerical solution of the voltage analytical function at s = 1 and the corresponding power state are used as the initial state to update and restart the PRHEM power flow model, n = n + 1 is set, and step b is returned; If the condition is not met, n = n + 1 is set, and step b is returned.

3. The power swing based full-purely embedded power flow algorithm of claim 1, wherein, The initial state of the model is updated as follows: The numerical solution of the voltage analytical function obtained at s = 1 of the classical HEM model or the PRHEM model obtained after the first start is used as the voltage initial solution of the PRHEM power flow model after the restart update, the power obtained by calculating the updated voltage initial value through formula (2) is used as the initial state power of the PRHEM power flow model after the restart update, and the restart update of the PRHEM power flow model is realized.

4. The power swing based full-purely embedded power flow algorithm of claim 1, wherein, The PRHEM power flow model is solved as follows: The recursive calculation matrix equation of each node model is obtained according to the power series coefficient equivalence principle; Balanced node: where Re(·) is the real part function; Im(·) is the imaginary part function; V i [n] is the voltage analytic function V i the n-th order coefficient of V n0 and δ n1 is the impulse function, which means the function value is 1 if and only if the subscript n = 0 and n = 1. PQ node where G i,k , B i,k are the real and imaginary parts of Y i,k , which represents the conductance and susceptance relationship between node i and node k; the expression for the auxiliary variable K[n-1] is as follows: where the variable parameters in the brackets represent the corresponding power of the coefficient; W i [·] is the power series coefficient of the auxiliary holomorphic function i (s), W i (s) is the inverse form of V i (s) to help the Taylor expansion of the equation with denominator V i (s) in the model; PV node where Q i [n] is the PV node reactive power analytical function Q i of order n of the function (s); the superscripts Re and Im denote the real and imaginary parts of the variable, respectively; the auxiliary variables L[n-1], D[0] and M[n-1] are given by: The recursive matrix equation of the power flow model is constructed, and formula (8), (9) and (12) are comprehensively used, and based on the matrix transformation technology, the following matrix equation can be obtained: where the subscripts VS, PQ and PV represent the numbers of the equilibrium, PQ and PV nodes, respectively, corresponding to the node numbers i and k referred to above; and the auxiliary variable may be expressed as: may be expressed as: By means of equation transformation and equation replacement, the Q PV [n] is moved to the left side of the equation, and the expression of is replaced by The equation unknown variables are all on the left side of the equation, and the known quantities are all on the right side of the equation; the following equation is obtained: The recursive matrix equation calculation form of the final power flow model can be represented as: AX = b (17) In the formula, A is a linear equation coefficient matrix generated by a recursive calculation process; X is a model to-be-sought power series coefficient vector; and b is a known vector calculated by not more than n-1 order coefficients.

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