A holomorphic-embedded power system power flow method considering engineering constraints

Abstract

The application provides a full-pure embedded power system flow method considering engineering constraints, comprising obtaining power grid data and establishing a flow calculation model; performing model conversion based on the flow calculation model, establishing a pseudo-gradient system, and calculating stable equilibrium manifolds of the pseudo-gradient system; searching for all stable equilibrium manifolds in a layer-by-layer search manner, and screening out flow solutions meeting specific conditions; calculating the distance between the flow solutions and boundary values ensuring stable operation of the power system, and judging whether the distance meets a required reserved margin; if not, planning relevant dispatching strategies of increasing power generation and reducing load. The application establishes a corresponding polynomial model for the power system flow problem considering engineering constraints, efficiently solves the power system flow problem with constraints, and is used for power system state analysis; and through uniformly distributed search directions, the possibility of repeatedly entering the same convergence domain caused by searching from similar directions can be significantly reduced, and the search efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system, and particularly relates to a full-pure embedded power system power flow method considering engineering constraints. BACKGROUND

[0002] As the core of the power industry, the power system power flow problem is considered as one of the most important problems in the design and operation of the power system, which involves bus voltage, current and power. The power flow equation describes the relationship between complex bus voltage and active and reactive power injection under steady state, which can be expressed as a polynomial system in rectangular coordinates, and for a given set of parameters, the system often has multiple complex solutions, but only a few real solutions that meet certain conditions have application value in engineering practice. For example, when carrying out power system power flow calculation, the power flow solution with a small change in the rated voltage difference meets the requirements of normal system operation.

[0003] For calculating the real solutions of the polynomial system with constraints, the existing methods mainly adopt the following three schemes:

[0004] 1. Calculating the resultant of the polynomial system. Although this scheme has a solid mathematical theory as support, the calculation of the resultant of the polynomial equation set is an NP-hard problem, and the existing technology mainly uses this scheme to deal with the real solution problem of small-scale polynomial system with only a few variables, which is difficult to be applied to practical engineering calculation.

[0005] 2. Selecting or randomly generating several points as initial points for iterative calculation in or near the feasible region determined by the constraint conditions. Using traditional iterative methods such as Newton method, it is possible to search for a real solution of the polynomial system (with constraints). However, considering that the convergence domain of the traditional iterative method is usually irregular, and its boundary has a fractal structure, it is generally difficult to predict the location of the solution obtained by the final search according to the initial point, and there is also a lack of solid mathematical theory to guarantee the completeness of the solution set.

[0006] 3. First, find all complex solutions by extending the polynomial in complex space, and then select real solutions that meet the requirements. This method has two obvious drawbacks: First, for large-scale problems, the number of all complex solutions is very large, and the homotopy extension method often struggles to calculate the upper bound of the number of solutions using the mixed-volume method, making it difficult to construct the initial system and its initial solution set. Second, even if the corresponding initial system and its initial solution set can be constructed, on the one hand, existing polynomial system computation tools mainly use the prediction-correction framework to implement the homotopy extension method, which often leads to problems such as path jumps, resulting in missed solutions. It is also difficult to implement the extension in real space. For example, when encountering a saddle-node bifurcation point in the extension path, the Jacobian matrix is ​​singular, making it difficult to predict the extension direction and thus impossible to numerically complete the homotopy extension. On the other hand, if all complex solutions are calculated by extending the polynomial in complex space, and then real solutions that meet specific conditions are selected, since the proportion of real solutions that meet specific conditions is often very low, most of the computational resources will be spent on calculating non-real solutions, resulting in a significant reduction in computational efficiency. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a fully embedded power flow method for power systems that considers engineering constraints. This invention can efficiently solve power flow problems with constraints, so as to be used for power system state analysis.

[0008] The technical solution of this invention is: a fully embedded power flow method for power systems considering engineering constraints, comprising the following steps:

[0009] S1) Obtain power grid data and establish a power flow calculation model;

[0010] S2) Based on the power flow calculation model, perform model transformation and establish a pseudo-gradient system, and calculate the stable equilibrium manifold of the pseudo-gradient system;

[0011] S3) Based on a hierarchical search method, find all stable equilibrium manifolds and filter out the power flow solutions that meet specific conditions;

[0012] S4) Calculate the distance between the power flow solution and the boundary value that ensures the stable operation of the power system, and determine whether the distance meets the required reserve margin; if not, plan relevant dispatch strategies to increase power generation and reduce load.

[0013] Preferably, in step S1), the power flow calculation equation is first established at node i of PQ:

[0014]

[0015] In the formula, V represents the voltage at node i, respectively. ithe real and imaginary parts of the voltage V ik ik are the conductance and susceptance between nodes i and k, respectively i i are the real and imaginary parts of the voltage V

[0016] As preferred, in step S1), the power flow equation is then established at the PV node i:

[0017]

[0018] wherein, are the real and imaginary parts of the voltage V i at node i; i, k are the node numbers, respectively; n is the total number of nodes; G ik ik are the conductance and susceptance between nodes i and k, respectively i is the real power of node i; V i,sp represents the given voltage amplitude of node i.

[0019] As preferred, in step S1), after the power flow equation is established, a constraint is added to the voltage V i , i.e.:

[0020]

[0021] As preferred, in step S2), the expression of the pseudo-gradient system is established as:

[0022]

[0023] wherein, H(x) is a vector function determined by the original equation set and the constraint condition, DH(x) represents the Jacobian matrix of H(x), and the superscript T represents the transpose of the matrix.

[0024] As preferred, in step S2), the stable equilibrium manifold of the pseudo-gradient system is calculated by using the logarithmic method, and the power series expansion of the solution function x k (t) at any t=t0 is substituted into formula (4), the power series coefficients a kq are calculated by comparing the coefficients of the same power of (t-t0).

[0025] wherein, the expression of the power series expansion is:

[0026] x k (t) =∑ q≥0 a kq (t-t0) q , 1≤k≤m+d.​​​

[0027] As preferred, in step S2), after a stable equilibrium manifold of the pseudo-gradient system is calculated, the escape point is calculated to jump out of the convergence domain of the current stable equilibrium manifold to search for another stable equilibrium manifold.

[0028] The present application has the following advantages:

[0029] 1. The present application establishes a corresponding polynomial model for the power system load flow problem considering engineering constraints, efficiently solves the power system load flow problem with constraints, and is used for power system state analysis.

[0030] 2. The present application converts the task of solving real solutions of a polynomial system into the problem of solving stable equilibrium manifolds of a pseudo-gradient dynamic system by model conversion, directly searches for all real solutions of the polynomial system with constraints in the real number field, and overcomes the defect that the existing screening method cannot calculate real solutions when dealing with super-large problems due to difficulty in constructing an initial system and an initial solution set.

[0031] 3. The present application uses vectors composed of points uniformly distributed on a unit sphere and the origin as search directions, which can significantly reduce the possibility of repeatedly entering the same convergence domain from similar direction sets, and improve search efficiency.

[0032] 4. The present application uses the logarithmic method to calculate the coefficients of the power series expansion, which can reduce the combination number time complexity of the commonly used convolution method to linear time complexity.

[0033] 5. The present application uses piecewise rational functions for approximation, which can construct a high-precision approximate numerical solution function, rather than just get a finite number of discrete points on the solution curve of the pseudo-gradient system. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 It is a framework structure diagram of the present application;

[0035] Figure 2 It is a flowchart of the method of the present application;

[0036] Figure 3 It is a flowchart of the present application for searching for all stable equilibrium manifolds layer by layer;

[0037] Figure 4 It is a flowchart of the present application for searching for stable equilibrium manifolds of adjacent layers;

[0038] Figure 5 It is a flowchart of the present application for calculating escape points;

[0039] Figure 6Flowchart for calculating single stable equilibrium manifold for the present application. DETAILED DESCRIPTION

[0040] The specific embodiments of the present application are further described below with reference to the accompanying drawings:

[0041] As shown in Figure 1 and 2 , the present embodiment provides a holomorphic embedded power system power flow method considering engineering constraints, comprising the following steps:

[0042] S1), obtaining power grid data and establishing a power flow calculation model;

[0043] S2), model conversion based on the power flow calculation model and establishment of a pseudo-gradient system, and calculation of the stable equilibrium manifold of the pseudo-gradient system;

[0044] S3), searching for all stable equilibrium manifolds based on a layer-by-layer search method, and screening out power flow solutions that meet specific conditions;

[0045] S4), calculating the distance between the power flow solution and the boundary value for ensuring stable operation of the power system, and judging whether the distance meets the required reserved margin; if not, planning relevant dispatching strategies for increasing power generation and reducing load.

[0046] As preferred in the present embodiment, in step S1), first, the power flow calculation equation is established at the PQ node i:

[0047]

[0048]

[0049] In the formula, respectively represent the real part and the imaginary part of the voltage V i at the node i; i, k respectively represent the node number; n is the total number of nodes; G ik , B ik are the conductance and the susceptance between the nodes i and k; P i , Q i are the real power and the reactive power of the node i, wherein the node 1 is a slack node, whose voltage is fixed and known.

[0050] As preferred in the present embodiment, in step S1), then the power flow calculation equation is established at the PV node i:

[0051]

[0052] In the formula, respectively represent the real part and the imaginary part of the voltage V i at the node i; i, k respectively represent the node number; n is the total number of nodes; Gik B ik are conductance and susceptance between nodes i and k, respectively; P i is real power at node i; V i,sp denotes given voltage magnitude at node i.

[0053] As preferred in the embodiment, in step S1), after establishing the power flow equation, a constraint is added to the voltage V i , i.e.:

[0054]

[0055] Then, equations (1) and (2) with constraint (3) are uniformly expressed as:

[0056] F(z) = (F1(z), …, F m (z)) T = 0, s.t. T(z)≤0;

[0057] where z = (z1, …, z m ) T denotes unknown quantity, and m is the number of unknown quantities, satisfying m = 2n-2;

[0058] 1≤l≤m denotes equations (1) and (2), denotes real number field, denotes real polynomial, and l is an index; T(z) = (T1(z), …, T d (z)) T denotes constraint condition, 1≤l≤d denotes inequalities (3), and d = 2n-2 is the number of inequality constraints.

[0059] As preferred in the embodiment, in step S1), the inequality constraint is converted into a polynomial equality constraint by adding a slack variable, and the expression of the polynomial equality constraint is:

[0060]

[0061] where y = (y1, …, y d ) T ; y l is a slack variable, is an augmented variable; is the converted equality constraint;

[0062] further converted into calculating real solutions of the augmented polynomial system ; and uniformly expressed as calculating H(x) = (H1(x), …, H m+d (x)) Treal solutions of x = 0, where x is the unknown to be solved, 1≤k≤m+d;

[0063] Since the number of unknowns of the augmented polynomial system H(x) = 0 is the same as the number of equations, only isolated real solutions are considered.

[0064] As preferred in the present embodiment, in step S2), the expression of the pseudo-gradient system established is:

[0065]

[0066] In the formula, DH(x) represents the Jacobian matrix of H(x), and the superscript T represents the transpose of the matrix.

[0067] As preferred in the present embodiment, in step S2), the stable equilibrium manifold of the pseudo-gradient system is calculated by using the logarithmic method, and the solution function x k (t) is substituted into formula (4) at any t = t0, and the power series coefficients a kq are calculated by comparing the coefficients of the same power of (t - t0). k q≥0 kq q 1≤k≤m+d;

[0068] In the formula, the expression of the power series expansion is:

[0069] x k (t) = ∑ q≥0 a kq (t - t0) q , 1≤k≤m+d;

[0070] By constructing a rational approximation function according to the existing power series information, the convergence domain is expanded, and the rational approximation value and its derivative value calculated at t = t0 + Δt = t0 + Δt * are substituted into formula (4); whether the difference between the left and right sides is greater than the pre-set tolerable threshold value is compared; Δt is found to make the difference between the left and right sides of formula (4) less than the pre-set tolerable threshold value; t0 is updated as t0←t0+Δt, until the solution of Q H (x) = 0 is obtained; where t represents the time variable of the pseudo-gradient system, t0 represents the t value expanded at any point; Δt represents the effective interval length, and Δt * is the initial interval length of each expansion.

[0071] As preferred in the present embodiment, in step S2), when one stable equilibrium manifold of the pseudo-gradient system is calculated, the method of calculating escape points is used to jump out of the convergence domain of the current stable equilibrium manifold to find another adjacent stable equilibrium manifold.

[0072] As preferred in the present embodiment, in step S2), as Figure 6As shown, the stable equilibrium manifold of the pseudo-gradient system is calculated by logarithmic method, and comprises the following steps:

[0073] S211), initialization, setting the order q of the power series part of * , the allowable threshold value ε EM , the initial interval length Δt of each expansion * , the reduction ratio The initial point x0=(x1(0),…,x m+d (0)), and the initial point t0=0.

[0074] S212), parameterization by t, and expressing the solution function x(t) of the pseudo-gradient system as x(t), wherein the solution function x(t) of the pseudo-gradient system satisfies:

[0075]

[0076] S213), assuming that the solution function x(t) of the pseudo-gradient system is holomorphic near t=t0, and the series expansion of x(t) at t0 is expressed as:

[0077] x k (t)=Σ q≥0 a kq (t-t0) q ,1≤k≤m+d,

[0078] wherein a kq is the power series coefficient;

[0079] Assuming that the series expansion of Q H (x(t)) at t0 is expressed as:

[0080] Q H,k (x(t))=∑ q≥0 Q H,kq (t-t0) q ,1≤k≤m+d,

[0081] wherein Q H,k (x(t)) is the kth element of Q H (x(t)), and Q H,kq is the power series coefficient of Q H,k (x(t));

[0082] S214), substituting the power series into equation (5), comparing the coefficients of (t-t0) q on both sides of the equation, and sequentially solving the power series coefficients a kq for q≥0;

[0083] S215), comparing the coefficients of (t-t0) 0 on both sides of the equation, and solving ak0 (k = 1,..., m + d) have:

[0084] a k0 = x k (t0), 1≤k≤m+d;

[0085] S216), compare both sides of the equation (t - t0) q , q≥1, get:

[0086] qa kq = Q H,k(q-1) ;

[0087] The specific steps of solving the power series coefficient by logarithmic method are as follows: for each monomial Satisfy the following three expressions:

[0088]

[0089]

[0090]

[0091] Where and are the power series expansion coefficients of the logarithmic variable, the logarithmic monomial and the monomial respectively. According to x k (t) is the coefficient of the first q+1 power of The steps to solve the power series expansion q+1 power coefficient of monomial

[0092] From equation (6), we get

[0093]

[0094] From equation (7), we get

[0095]

[0096] From equation (8), we get

[0097]

[0098] Where 1≤k≤m+d; since Q H,k (x(t)) is a linear combination of monomials , Q H,k(q+1) is also a linear combination of , so Q H,k(q+1) can be calculated. Then according to sequence (12) to solve a kq , Q H,kq :

[0099]

[0100] S217), the corresponding coefficient a is calculated kq q≤q * , the truncated power series is adopted:

[0101] 1≤k≤m+d,

[0102] and the corresponding rational approximation and the corresponding derivative are calculated, i.e.:

[0103]

[0104] wherein L and N are the orders of the numerator and the denominator of the rational approximation respectively, and satisfy L+N=q * ; the derivative is represented by δ kq , respectively, are the coefficients of the numerator and the denominator of the rational approximation, and satisfy δ k0 =1;

[0105] S218), the initial interval length Δt=Δt * >0; it is checked whether the maximum error of equation (5) on t∈[t0,t0+Δt] is less than the pre-set tolerable error threshold ∈ EM ;

[0106] If yes, the effective interval is determined as [t0,t0+Δt]; otherwise, the interval length is reduced to until yes is satisfied; t0 is updated as t0←t0+Δt;

[0107] S219), steps S213) to S218) are repeated until the value of the energy function at t0 is less than 0.1 at the initial point, then a local solver is adopted to calculate the solution of Q H (x)=0.

[0108] As preferred in the embodiment, in step S2), as shown in Figure 5 , the escape point is calculated to find the other adjacent stable equilibrium manifold, which specifically includes the following steps:

[0109] S221), the initial stable equilibrium point X s , the search path direction d, the search step length Δt>0, and the search stop maximum value F Lim >0 are initialized;

[0110] S222), starting from x s , the initial iteration point is taken as a small perturbation point on the search path direction d Let the iteration number i=0;

[0111] S223), Calculation

[0112] S224), respectively calculated in The inner product of the derivative of the search path at a point and the vector field of the pseudo-gradient system, i.e., d and -DH(x). T The inner product of H(x) is denoted as

[0113] S225), update i←i+1;

[0114] S226), Repeat steps S223) to S225) until one of the following conditions is met;

[0115] 1) Returns a message indicating successful solution and

[0116] 2) Functions The value of i or the value of i is greater than the given F. Lim Returns a solution failure and

[0117] In a preferred embodiment, in step S3), as follows: Figure 3 As shown, all stable equilibrium manifolds are found through a layer-by-layer search, and the corresponding power flow solutions are selected from the obtained stable equilibrium manifolds, including the following steps:

[0118] S31) Initialize the initial point x0, search step size Δt>0, and search stopping maximum value F. Lim >0, Number of search paths N * >0;

[0119] S32) Starting from the initial point x0, a stable equilibrium manifold of the pseudo-gradient system calculated in step S2) is obtained.

[0120] S33), Set the stable equilibrium manifold set as The set of stable equilibrium manifolds at layer 0 is: The set of escape points is k = 0;

[0121] S34), Set the set of stable equilibrium manifolds at the (k+1)th layer as...

[0122] S35), for Each stable equilibrium manifold Find the stable equilibrium manifold of all its adjacent layers;

[0123] S36) Judgment Is it equal to If yes, go to step S37); otherwise, k <- k + 1, go to step S34);

[0124] S37), find a stable equilibrium manifold x SEM for each of the stable equilibrium manifold x s , and determine whether it is a solution of the polynomial system H(x) = 0.

[0125] As preferred in the present embodiment, as shown in FIG. 5, in step S35), finding a stable equilibrium manifold of the adjacent layer specifically includes the following steps: Figure 4

[0126] S351), construct N * straight line search paths according to the uniform distribution of the unit sphere 1≤i≤N * ; set i = 1;

[0127] S352), along the search path of x , find a corresponding escape point by using the step of finding an escape point; if the escape point is successfully found, go to step S353); otherwise, go to step S356);

[0128] S353), define the successfully found escape point as x and determine whether x belongs to V ex ; if yes, go to step S356); otherwise, update x and go to step S354);

[0129] S354), starting from x , solve the pseudo-gradient system to obtain a stable equilibrium manifold x and determine whether the solving is successful; if successful, go to step S355); otherwise, go to step S356);

[0130] S355), determine whether x belongs to V SEM ; if not, update x

[0131] S356), i <- i + 1;

[0132] S357), repeat steps S352)-S356) until i > N * .

[0133] ​​​The foregoing embodiments and description of the application only illustrate the principle and the best mode of the application, and various changes and modifications can be made to the application without departing from the spirit and scope of the application, and all these changes and modifications fall within the scope of the application.

Claims

1. A holomorphic-embedded power system power flow method considering engineering constraints, characterized in that, The method comprises the following steps: S1), obtaining power grid data and establishing a power flow calculation model; S2), performing model conversion based on the power flow calculation model, establishing a pseudo-gradient system, and calculating a stable equilibrium manifold of the pseudo-gradient system; The expression of the established pseudo-gradient system is as follows: In the formula, H(x) is a vector function determined by the original equation set and the constraint condition, DH(x) represents the Jacobian matrix of H(x), the superscript T represents the transpose of the matrix; x is an unknown quantity to be solved; t represents a time variable of the pseudo-gradient system; The stable equilibrium manifold of the pseudo-gradient system is calculated by using the logarithmic method, and the solution function x k (t) is substituted into equation (4) at any t = t0, and the power series coefficients a kq are calculated by comparing the coefficients of the same power of (t - t0). The expression of the power series expansion is as follows: x k (t) =∑ q≥0 a kq (t-t0) q ,1≤k≤m+d; In the formula, m is the number of unknown quantities, and m=2n-2 is satisfied; d=2n-2 is the number of inequality constraints; n is the total number of nodes; k represents the number of solution functions; q is the order; S3), searching for all stable equilibrium manifolds in a layer-by-layer search manner, and screening out power flow solutions meeting specific conditions; S4), calculating the distance between the power flow solution and the boundary value for ensuring stable operation of the power system, and judging whether the distance meets a required reserved margin; if not, relevant dispatching strategies for increasing power generation and reducing load are planned.

2. The method of claim 1, wherein the method is a method of full-pure embedded power system power flow considering engineering constraints. In step S1), the power flow calculation equation is first established at the PQ node i: wherein Re(i) and Im(i) represent the real and imaginary parts of the voltage V i at node i, respectively; i, k represent the node numbers, respectively; n is the total number of nodes; G ik and B ik are the conductance and susceptance between nodes i and k, respectively; P i and Q i are the real and imaginary powers at node i, respectively.

3. The method of claim 2, wherein: In step S1), the power flow calculation equation is then established at the PV node i: wherein Re(Vi) and Im(Vi) represent the real and imaginary parts of the voltage V i at node i; i, k represent the node numbers; n is the total number of nodes; G ik and B ik are the conductance and susceptance between nodes i and k; P i is the real power at node i; V i,sp represents the given voltage magnitude at node i.

4. The method of claim 3, wherein: In step S1), after the power flow equations are established, the voltage V i Add the constraint that:

5. The method of claim 1, wherein: In step S2), after a stable equilibrium manifold of the pseudo-gradient system is calculated, the escape point is calculated to jump out of the convergence domain of the current stable equilibrium manifold to search for another adjacent stable equilibrium manifold. By using the vectors composed of the uniformly distributed points on the unit sphere and the origin as the search direction, the possibility of repeatedly entering the same convergence domain from a similar direction set is significantly reduced, and the search efficiency is improved.

6. The method of claim 1, wherein: In step S2), the stable equilibrium manifold of the pseudo-gradient system is calculated by using the logarithmic method, and the specific steps include the following steps: S211) initialization, setting the order q of the power series part * , allowable threshold value ε EM , initial interval length Δt of each expansion * , reduction ratio initial point x0 = (x1(0),..., x m+d (0)), initial point t0 = 0 S212), the solution function of the pseudo-gradient system is expressed as x(t) by using t for parameterization, and the solution function x(t) of the pseudo-gradient system satisfies: S213), it is assumed that the solution function x(t) of the pseudo-gradient system is holomorphic near t=t0, and the series expansion of x(t) at t0 is expressed as follows: x k (t) =∑ q≥0 a kq (t-t0) q ,1≤k≤m+d wherein a kq are the power series coefficients; Assume Q H The series expansion of (x(t)) at t0is expressed as follows: Q H,k (x(t)) =∑ q≥0 Q H,kq (t-t0) q ,1≤k≤m+d, where Q H,k (x(t)) is the kth element of Q H (x(t)), Q H,kq is the power series coefficient of Q H,k (x(t)). S214), substituting the power series into equation (5), comparing both sides of the equation (t - t0) q , the coefficients of q > 0 are solved in turn to obtain the power series coefficients a kq ; S215), compare both sides of the equation (t-t0) 0 the coefficient of a k0 (k = 1,..., m + d) have: a k0 = x k (t0),1≤k≤m+d; S216), compare both sides of the equation (t - t0) q q ≥ 1, the coefficient, resulting in: qa kq = Q H,k(q-1) ; S217), the corresponding coefficient a is calculated kq q ≤ q * The truncated power series is used The corresponding rational approximation and the corresponding derivative are calculated, that is, where L, N are the orders of the numerator and denominator of the rational approximation, respectively, and satisfy L + N = q * ;'denotes the derivative, δ kq are the coefficients of the numerator and denominator of the rational approximation, respectively, and satisfy δ k0 = 1. S218), let the initial interval length Δt = Δt * > 0; check whether the maximum error of equation (5) over t ∈ [t0, t0+ Δt] is smaller than a pre-set tolerable error threshold ∈ EM ; If yes, determine the valid interval as [t0, t0+Δt]; otherwise, reduce the interval length by until yes; update t0←t0+Δt; S219), repeating steps S213) to S218) until the energy function The value at t0is less than 0.1 at the initial point, then a local solver is employed to calculate Q H (x) = 0.

7. The method of claim 6, wherein the method is a method of full-pure embedded power system power flow considering engineering constraints. In step S2), the escape point is calculated to search for another adjacent stable equilibrium manifold, and the specific steps include the following steps: S221), initialize the initial stable equilibrium point x s , search path direction d, search step size Δt > 0, search stop maximum value F Lim > 0; S222), from x s Starting from the search path direction d with a small perturbation point as the initial iteration point Let the iteration number i = 0; S223), compute S224), respectively, the inner product of the derivative of the search path at the point with the pseudo-gradient system vector field, i.e. d with -DH(x) T the inner product of H(x), denoted by S225), updating i←i+1; S226), repeating steps S223) to S225) until one of the following conditions is met; 1)、 Returning to the case where the solution is successful and 2) the function the value of i is greater than the given F Lim , return failure to solve and 8. The method of claim 7, wherein the method is a method of full-pure embedded power system power flow considering engineering constraints. In step S3), all stable equilibrium manifolds are searched for in a layer-by-layer search manner, and the corresponding power flow solutions are screened out from the obtained stable equilibrium manifolds, including the following steps: S31), initialize initial point x0, search step size At > 0, search stop maximum value F Lim > 0, search path number N * > 0; S32) from the initial point x0, a stable equilibrium manifold of the system of pseudo-gradients calculated in step S2) is adopted S33), set the stable equilibrium manifold set as The stable equilibrium manifold set of the 0th layer is The escape point set is k = 0; S34), set the stable equilibrium manifold set of the k+1th layer as S35) for each stable equilibrium manifold find all stable equilibrium manifolds of each of its adjacent layers find all stable equilibrium manifolds of each of its adjacent layers S36), determine whether equal to If yes, go to step S37); otherwise, k <- k + 1, go to step S34); S37), to V SEM each stable equilibrium manifold x s , determine whether it is a solution of the polynomial system H(x) = 0.

Images