A DC optimal power flow assessment method for power systems based on quasi-interior point embedding and hybrid accuracy

Abstract

This invention provides a method for evaluating optimal DC power flow in power systems based on quasi-interior point embedding and mixed precision. The method includes acquiring grid data and establishing a DC optimal power flow calculation model; constructing a quasi-interior point embedding system; obtaining the optimal solution by solving the quasi-interior point embedding system using fast, flexible, fully pure embedding, and mixed precision methods; and evaluating the optimal DC power flow scheduling scheme based on the optimal solution. This invention constructs a quasi-interior point embedding system based on the idea that the control iteration points of the interior point method move along the central path towards the constraint boundary and the optimal solution. This allows for flexible selection of initial values ​​and leverages the characteristic that the central path of the interior point method always lies within the feasible region, thus ensuring that the quasi-interior point embedding system ultimately obtains the optimal feasible solution. By employing piecewise low-order approximation, computational efficiency is effectively improved. The use of mixed precision techniques to solve linear equations reduces computation time and resource consumption while ensuring the accuracy and stability of the solution, providing a more efficient and accurate optimization scheduling scheme.

Description

Technical Field

[0001] This invention relates to the field of power system planning, dispatching and operation and maintenance technology, and in particular to a method for evaluating the optimal DC power flow of a power system based on quasi-interior point embedding and hybrid accuracy. Background Technology

[0002] Optimal Power Flow (OPF) is one of the fundamental problems in power system optimization and scheduling. Its core research content is to optimize the scheduling and operation of the power system, reduce energy losses, and obtain a power flow distribution with lower generation costs while ensuring the safe and stable operation of the system. Optimal power flow is a typical non-convex optimization problem, and its solution is NP-hard, with no guarantee of global convergence or completion in polynomial time. To improve computational efficiency and enhance convergence, nonlinear AC optimal power flow is often approximated by a linearized DC optimal power flow (DC-OPF) problem. The DC-OPF model approximates the nonlinear characteristics of the power system, assuming constant voltage amplitude and neglecting the influence of reactive power.

[0003] With the expansion of power system scale, the number of nodes and lines in the power grid is growing exponentially. Bottlenecks in computational efficiency and resource consumption are becoming increasingly apparent in DC-OPF solution methods based on traditional iterative approaches (such as the interior-point method). The interior-point method is highly sensitive to the choice of initial points; improper selection can lead to convergence difficulties. Furthermore, it is highly dependent on the iteration step size in practical calculations, requiring multiple calculations and adjustments to find the optimal solution, resulting in low computational efficiency and hindering the solution of complex problems. Another approach is the fully embedded method based on non-iterative principles. Its main steps include constructing a suitable embedded system based on the target problem, obtaining the series expansion of the solution function of the embedded system, and calculating high-quality approximations using the series expansion. Extensive numerical experiments demonstrate that the fully embedded method is more robust and efficient than classical iterative methods in solving power flow problems.

[0004] While fully embedded methods can theoretically provide relatively accurate solutions, practical computation requires constructing a suitable embedded system based on the target problem. Furthermore, to meet accuracy requirements, higher-order terms in the series expansion need to be continuously calculated, directly impacting the method's convergence, stability, and computational efficiency. Improperly constructed embedded systems or excessively high-order expansion coefficients can lead to numerical instability, slow convergence, and low computational efficiency, preventing the system from making timely optimization decisions and thus affecting the safety and real-time performance of power grid dispatch. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a DC-OPF (Dynamic Optimal Power Flow) assessment method for power systems based on quasi-interior point embedding and mixed precision. This invention addresses the DC-OPF problem through steps such as constructing a quasi-interior point embedding system, piecewise rational approximation, and mixed precision acceleration. It combines efficient numerical computation methods with modern hardware acceleration technology, providing strong support for the real-time performance and accuracy of large-scale power system optimization scheduling. Furthermore, this invention offers advantages such as faster computation speed, better convergence, and stronger robustness, better meeting the requirements of new power system planning and scheduling.

[0006] The technical solution of this invention is: a DC optimal power flow evaluation method for power systems based on quasi-interior point embedding and hybrid accuracy, comprising the following steps:

[0007] S1) Obtain power grid data and establish a DC optimal power flow calculation model;

[0008] S2) Construct a pseudo-interior point embedding system based on the DC optimal power flow calculation model;

[0009] S3) The optimal solution is obtained by solving the quasi-interior point embedding system based on fast and flexible pure embedding and mixed precision;

[0010] S4) Evaluate the optimal DC power flow scheduling scheme based on the optimal solution.

[0011] Preferably, in step S1), the DC optimal power flow calculation model is established, which specifically includes the following steps:

[0012] S11) Obtain grid data and determine the objective function based on the power generation cost data of the generator sets;

[0013] S12) Determine the constraint set based on the power grid data;

[0014] S13) Establish a DC optimal power flow calculation model based on the objective function and constraint set.

[0015] Preferably, in step S11), the expression of the objective function is:

[0016] (1);

[0017] in, The voltage phase angle at each node; The active power of the generator set. For the number of nodes, Number of generator sets; For cost function, For generator sets Those who have made contributions For generator sets The coefficients of the first-order term of the cost function; This is the set of coefficients for the first-order term of the cost function of the generator set; = Represents the augmentation coefficient vector; These are decision variables.

[0018] Preferably, in step S12), the constraint set includes equality constraints and inequality constraints.

[0019] Preferably, in step S12), the equality constraints for the optimal DC power flow problem are determined through the nodal power balance equations, namely:

[0020] (2);

[0021] In the formula, Here is the nodal admittance matrix; The voltage phase angle at each node; For the active load of the power system, For the adjacency matrix of nodes and generator sets: when generator sets Connected to the node When, adjacency matrix The Line number Column elements The value is 1 if it is set to 1, otherwise the value is 0. This refers to the active power of the generator set.

[0022] Preferably, in step S12), the inequality constraint set for the optimal DC power flow problem is determined by the output limit of the generator set and the transmission power limit of the transmission line; that is:

[0023] ; (3)

[0024] ;

[0025] In the formula, These are the minimum and maximum values ​​of the active power that the generator set is allowed to output, respectively. Here is the branch admittance matrix; This represents the maximum allowable power transmission capacity of a power transmission line.

[0026] Preferably, in step S13), the expression for the DC optimal power flow calculation model is:

[0027]

[0028] (4)

[0029]

[0030] in,

[0031] ;

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] Since the DC-OPF model assumes a very small voltage phase angle difference and that the voltage phase angle of the reference node is 0, it can be set as follows: Voltage phase angle The minimum and maximum values.

[0037] Preferably, in step S13), a translation variable is introduced. and slack variables Equation (4) is equivalently transformed into a standard linear programming problem; that is:

[0038]

[0039] (5)

[0040]

[0041] in,

[0042] ;

[0043] in, It is a diagonal matrix. For constraint numbers; Number of variables.

[0044] Preferably, in step S2), constructing the quasi-interior point embedding system based on the DC optimal power flow calculation model includes the following steps:

[0045] S21), let for The dual variable, introducing parameters ;

[0046] S22), for any satisfying initial point The design of the pseudo-interior point embedding system is as follows:

[0047] (6)

[0048] In the formula, It is a coefficient matrix; ; These represent the embedded parameters respectively. A vector function with variables; , It is a diagonal matrix, and its diagonal elements are respectively , .

[0049] S23), when At that time, take ;along with from Gradually towards near, The value of gives a homotopy path that gradually approximates the solution to the original problem; when hour, That is what I wanted.

[0050] Preferably, in step S3), the optimal solution is obtained by solving the quasi-interior point embedding system based on fast, flexible, fully pure embedding and mixed-precision methods, as follows:

[0051] exist any point Place, will Expand into a power series:

[0052]

[0053]

[0054]

[0055] In the formula, It is the order of the power series; They are respectively correspond The coefficient of the term;

[0056] Substitute equation (7) into equation (6) and compare the left and right sides of the equation. The coefficients of the terms are used to obtain the unknown coefficients of the power series. The system of linear equations satisfied;

[0057] For the block structure of the coefficient matrix, the solution of the above linear equation system is calculated using a mixed precision method after simplification: first, an initial decomposition is performed in single precision, and then iterative improvement is performed using double precision; while maintaining the accuracy of the high-precision solution, the solution of the linear equation system is accelerated.

[0058] Then, based on the already obtained information about The power series expansion is used to construct a rational approximation function to expand the region of convergence; then, the solution path is found to satisfy equation (6) with an error less than the given allowable error and close to the given error. parameter values ,Will As a new starting point, Repeat the above steps until... .

[0059] Preferably, in step S3), the optimal solution is obtained by solving the quasi-interior point embedding system based on fast, flexible, fully pure embedding and mixed-precision methods, specifically including the following steps:

[0060] S31), Set the maximum order of the power series expansion to... The allowable error is Initial extension interval Minimum threshold of extended interval Reduction ratio Initial iteration point , extension initial point , Extend the endpoint ;

[0061] S32), Introducing parameters Construct a pseudo-interior point embedding system:

[0062] (6)

[0063] S33), Order At point General Represented as a power series expansion:

[0064]

[0065]

[0066] S34), will Substituting the power series expansion into the quasi-interior point embedding system, we obtain the equation with the coefficients of the power series expansion as unknowns:

[0067] ;

[0068] ;

[0069] S35), when hour, , , ;

[0070] S36), when When, the coefficients of the power series expansion The equations satisfied are a system of linear equations, which can be expressed as:

[0071] (9)

[0072] in, Represents the coefficient matrix; Denotes the coefficients of the power series expansion to be solved; Indicates the right-hand term; , , Let each represent a vector consisting of the coefficients of a power series expansion; , It is a diagonal matrix, and its diagonal elements are respectively , , It is the identity matrix;

[0073] when hour, ;

[0074] when hour, ;

[0075] in, It is a diagonal matrix, and its diagonal elements are respectively ;

[0076] S37), for the coefficient matrix The block structure simplifies the linear equation system (9) to:

[0077]

[0078] (10b)

[0079] (10c)

[0080] in, It is a symmetric positive definite matrix;

[0081] S38) Solving the linear equation system (10a) using mixed-precision techniques yields the following results: Then, using double precision calculations, we obtain (10b) and (10c). While maintaining the accuracy of high-precision solutions, it accelerates the solution process;

[0082] S39) Using the obtained power series expansion coefficients Construct rational approximation functions to expand the region of convergence;

[0083] S40) Determine when When, the equation Is the maximum error at both ends less than the allowable error? If satisfied, proceed to step S41; otherwise, narrow down the interval. until the condition is met;

[0084] S41), Order Repeat S33) to S40) until .

[0085] Preferably, step S38) specifically includes the following steps:

[0086] S381), Calculate the matrix The initial solution is obtained by back-substituting the LU decomposition in single-precision mode. ;

[0087] S382) Calculate residuals using double precision. ,Right now:

[0088]

[0089] In the formula,

[0090] S383), using the LU decomposition from step S381), calculate To obtain the correction direction ;

[0091] S384), Update ;

[0092] (S385) Repeat steps (S382) - (S384) until the maximum number of iterations is reached or the accuracy requirement is met, then output the solution. ;

[0093] S386) Using double precision calculation , Finally obtained .

[0094] Preferably, in step S4), the rational approximation of the last series expansion is performed... It is worthwhile to be there This leads to the optimal solution to the DC optimal power flow problem, thereby obtaining the DC optimal power flow scheduling scheme, including the optimal voltage phase angle of each node. and the optimal active power of the generator .

[0095] The beneficial effects of this invention are as follows:

[0096] 1. This invention is based on the idea of ​​controlling the iteration points to move closer to the constraint boundary and the optimal solution along the central path of the interior point method, and constructs a quasi-interior point embedding system, which can flexibly select the initial value; at the same time, it draws on the characteristic that the central path of the interior point method is always within the feasible region, so as to construct a quasi-interior point embedding system to ensure that it finally obtains the optimal feasible solution, and significantly reduces the infeasible solutions caused by the use of other embedding systems.

[0097] 2. This invention employs piecewise low-order approximation, which avoids the problems of numerical instability and large computational load that occur when calculating higher-order terms of series expansion in traditional fully pure embedding methods, thus effectively improving computational efficiency;

[0098] 3. This invention employs mixed-precision technology to solve linear equation systems, accelerating the calculation process and reducing computation time and resource consumption while ensuring the accuracy and stability of the solution, thereby providing a more efficient and accurate optimization scheduling scheme. Attached Figure Description

[0099] Figure 1 This is a flowchart illustrating the framework of the method of the present invention;

[0100] Figure 2 This is a schematic diagram of the process of the present invention for rapid and flexible fully pure embedding based on pseudo-interior point embedding and mixed accuracy;

[0101] Figure 3 This is a flowchart of the mixed-precision calculation of linear equations according to the present invention. Detailed Implementation

[0102] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0103] like Figure 1 As shown, this embodiment provides a method for evaluating the optimal DC power flow of a power system based on quasi-interior point embedding and hybrid accuracy, including the following steps:

[0104] S1) Obtain power grid data and establish a DC optimal power flow calculation model; specifically, this includes the following steps:

[0105] S11) Obtain grid data and determine the objective function based on the power generation cost data of the generator sets; the optimal power flow problem is to optimize the output power of each generator set and the adjustable factors such as the voltage of each node in the power system, and find the optimal power flow distribution so that the total power generation cost of the system is the most economical; the expression of the objective function is:

[0106] (1);

[0107] in, The voltage phase angle at each node; The active power of the generator set. For the number of nodes, Number of generator sets; For cost function, For generator sets Those who have made contributions For generator sets The coefficients of the first-order term of the cost function; This is the set of coefficients for the first-order term of the cost function of the generator set; Represents the augmentation coefficient vector; These are decision variables.

[0108] The decision variables mentioned The set of coefficients of the first term of the cost function of the generator set Active power of generator set Augmentation coefficient vector They are represented as follows:

[0109] ; ; ; ;

[0110] In the formula, express Zero-dimensional vector.

[0111] S12) Determine the constraint set based on the power grid data;

[0112] In this embodiment, the constraint set includes equality constraints and inequality constraints. The equality constraints for the optimal DC power flow problem are determined through the nodal power balance equations, namely:

[0113] (2);

[0114] In the formula, Here is the nodal admittance matrix; The voltage phase angle at each node; For the active load of the power system, For the adjacency matrix of nodes and generator sets: when generator sets Connected to the node When, adjacency matrix The Line number Column elements The value is 1 if it is set to 1, otherwise the value is 0. This refers to the active power of the generator set.

[0115] The inequality constraint set for the optimal DC power flow problem is determined by the output limitations of generator sets and the transmission power limitations of transmission lines; that is:

[0116] ; (3)

[0117] ;

[0118] In the formula, The voltage phase angle at each node; These are the minimum and maximum values ​​of the active power that the generator set is allowed to output, respectively. Here is the branch admittance matrix; This represents the maximum allowable power transmission capacity of a power transmission line.

[0119] S13) Establish a DC optimal power flow calculation model based on the objective function and constraint set. In this embodiment, the expression of the DC optimal power flow calculation model is:

[0120]

[0121] (4)

[0122]

[0123] in,

[0124] ;

[0125] ;

[0126] ;

[0127] ;

[0128] ;

[0129] Since the DC-OPF model assumes a very small voltage phase angle difference and that the voltage phase angle of the reference node is 0, it can be set as follows: These are the minimum and maximum values ​​of the voltage phase angle.

[0130] In addition, this embodiment introduces a translation variable. and slack variables The above problem can be equivalently transformed into a standard linear programming problem; that is:

[0131]

[0132] (5)

[0133]

[0134] in,

[0135] ;

[0136] in, It is a diagonal matrix. For constraint numbers; Number of variables.

[0137] S2) Constructing a pseudo-interior point embedded system based on the DC optimal power flow calculation model; specifically including the following steps:

[0138] S21), let for The dual variable, introducing parameters ;

[0139] S22), for any satisfying initial point The design of the pseudo-interior point embedding system is as follows:

[0140] (6)

[0141] In the formula, It is a coefficient matrix; ; These represent the embedded parameters respectively. A vector function with variables; , It is a diagonal matrix, and its diagonal elements are respectively , .

[0142] S23), when At that time, take ;along with from Gradually towards near, The value of gives a homotopy path that gradually approximates the solution to the original problem; when hour, That is what I wanted.

[0143] S3) The optimal solution is obtained by solving the quasi-interior point embedding system based on fast, flexible, fully pure embedding and mixed-precision methods; the details are as follows:

[0144] exist any point Place, will Expand into a power series:

[0145]

[0146]

[0147]

[0148] In the formula, It is the order of the power series; They are respectively correspond The coefficient of the term;

[0149] Substitute equation (7) into equation (6) and compare the left and right sides of the equation. The coefficients of the terms are used to obtain the unknown coefficients of the power series. The system of linear equations satisfied;

[0150] For the block structure of the coefficient matrix, the solution of the above linear equation system is calculated using a mixed precision method after simplification: first, an initial decomposition is performed in single precision, and then iterative improvement is performed using double precision; while maintaining the accuracy of the high-precision solution, the solution of the linear equation system is accelerated.

[0151] Then, based on the already obtained information about The power series expansion is used to construct a rational approximation function to expand the region of convergence; then, the solution path is found to satisfy equation (6) with an error less than the given allowable error and close to the given error. parameter values ,Will As a new starting point, Repeat the above steps until... .

[0152] like Figure 2 As shown, this embodiment obtains the optimal solution for the quasi-interior point embedding system based on fast, flexible, fully pure embedding and mixed-precision methods, specifically including the following steps:

[0153] S31), Set the maximum order of the power series expansion to... The allowable error is Initial extension interval Minimum threshold of extended interval Reduction ratio Initial iteration point , extension initial point , Extend the endpoint ;

[0154] S32), Introducing parameters Construct a pseudo-interior point embedding system:

[0155] (6)

[0156] S33), Order At point General Represented as a power series expansion:

[0157]

[0158]

[0159] S34), will Substituting the power series expansion into the quasi-interior point embedding system, we obtain the equation with the coefficients of the power series expansion as unknowns:

[0160] ;

[0161] ;

[0162] S35), when hour, , , ;

[0163] S36), when When, the coefficients of the power series expansion The equations satisfied are a system of linear equations, which can be expressed as:

[0164] (9)

[0165] in, Represents the coefficient matrix; Represents the variable to be determined; Indicates the right-hand term; , Let each represent a vector consisting of the coefficients of a power series expansion; , It is a diagonal matrix, and its diagonal elements are respectively , , It is an identity matrix.

[0166] when hour, ;

[0167] when hour, ;

[0168] in, It is a diagonal matrix, and its diagonal elements are respectively ;

[0169] S37), for the coefficient matrix The block structure simplifies the linear equation system (9) to:

[0170]

[0171] (10b)

[0172] (10c)

[0173] in, It is a symmetric positive definite matrix;

[0174] S38) Solving the linear equation system (10a) using mixed-precision techniques yields the following results: Then, using double precision calculations, we obtain (10b) and (10c). While maintaining the accuracy of high-precision solutions, it accelerates the solution process; for example... Figure 3 As shown, the specific steps include the following:

[0175] S381), Calculate the matrix The initial solution is obtained by back-substituting the LU decomposition in single-precision mode. ;

[0176] S382) Calculate residuals using double precision. ,Right now:

[0177] ;

[0178] S383), using the LU decomposition from step S381), calculate To obtain the correction direction ;

[0179] S384), Update ;

[0180] (S385) Repeat steps (S382) - (S384) until the maximum number of iterations is reached or the accuracy requirement is met, then output the solution. ;

[0181] S386) Using double precision calculation , Finally obtained .

[0182] S39) Using the obtained power series expansion coefficients Construct rational approximation functions to expand the region of convergence;

[0183] S40) Determine when When, the equation Is the maximum error at both ends less than the allowable error? If satisfied, proceed to step S41; otherwise, narrow down the interval. This continues until the conditions are met; specifically as follows:

[0184] like make (Repeat S40).

[0185] like The loop exited, and the calculation failed.

[0186] S41), Order Repeat S33) to S40) until .

[0187] S4) Evaluate the optimal DC power flow scheduling scheme based on the optimal solution;

[0188] This embodiment is based on the rational approximation of the last series expansion. It is worthwhile to be there This leads to the optimal solution to the DC optimal power flow problem, thereby obtaining the DC optimal power flow scheduling scheme, including the optimal voltage phase angle of each node. and the optimal active power of the generator .

[0189] The embodiments and descriptions above are merely illustrative of the principles and preferred embodiments of the present invention. Various changes and modifications may be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed.

Claims

1. A method for power system DC optimal power flow evaluation based on quasi- interior point embedding and mixed precision, characterized in that, The method comprises the following steps: S1), obtaining power grid data, and establishing a DC optimal power flow calculation model; S2), constructing a quasi- interior point embedding system based on the DC optimal power flow calculation model; comprising the following steps: S21), set For the dual variable of wherein, , , is a translation variable; , is a slack variable; S22), for any initial point that satisfies ; the design of the quasi- interior point embedding system is as follows: （6） wherein is a coefficient matrix; ; denote vector functions with the embedding parameters as arguments, respectively; , is a diagonal matrix with the diagonal elements , ; , ; ; ; ; ; active power of the power system; upper limit of power transmission of the transmission line; node admittance matrix; branch admittance matrix; adjacency matrix of the nodes and generator units; minimum and maximum values of active power allowed to be generated by the generator units, respectively; minimum and maximum values of voltage phase angle ; , = denotes an augmented coefficient vector, a set of coefficients of the first order term of the cost function of the generator units; a constraint number; a variable number; S23), when the value of ; as from gradually approaching, the value of gives a homotopy path gradually approaching the solution of the original problem; when , is the solution. S3), solving the quasi- interior point embedding system to obtain an optimal solution; S4), evaluating the DC optimal power flow dispatching scheme according to the optimal solution; According to the value of the last series expansion formula, the rational approximation at is obtained , that is, the optimal solution of the DC optimal power flow problem, so as to obtain the DC optimal power flow scheduling scheme, including the optimal voltage phase angle and the optimal active power of the generator .

2. The method of claim 1, wherein the method is based on quasi- interior point embedding and mixed precision for power system DC optimal power flow evaluation. In step S1), the DC optimal power flow calculation model is established, specifically comprising the following steps: S11), obtaining power grid data, and determining a target function according to the power generation cost data of the generator set; S12), determining a constraint set according to the power grid data; S13), establishing a DC optimal power flow calculation model according to the target function and the constraint set.

3. The method of claim 2, wherein the method is based on quasi- interior point embedding and mixed precision for power system DC optimal power flow evaluation. In step S11), the expression of the target function is: （1） wherein is the voltage phase angle of each node; is the active power of the generator set, is the number of nodes, is the number of generator sets; is the cost function, is the active power of the generator set , is the cost function of the generator set , is the set of the linear term coefficients of the cost function of the generator set; = denotes the augmented coefficient vector; = is the decision variable; T denotes the transpose operation.

4. The method of claim 3, wherein the method is based on quasi- interior point embedding and mixed precision for power system DC optimal power flow evaluation. In step S12), the constraint set comprises equality constraints and inequality constraints; wherein, The equality constraints of the DC optimal power flow problem are determined by the node power balance equation, that is: ； （2） In the formula, Here is the nodal admittance matrix; The voltage phase angle at each node; For the active load of the power system, For the adjacency matrix of nodes and generator sets: when generator sets Connected to the node When, adjacency matrix The Line 1 Column elements The value is 1 if it is set to 1, otherwise the value is 0. Let the active power of the generator set be the power output of the generator set; the inequality constraint set for the optimal DC power flow problem is determined by the output limit of the generator set and the transmission power limit of the transmission line; that is: ； （3） ； wherein are the minimum and maximum values of the active power allowed to be emitted by the generator set, respectively; is the branch admittance matrix; is the upper limit of the power allowed to be transmitted by the transmission line.

5. The method of claim 4, wherein: In step S13), the expression of the DC optimal power flow calculation model is: （4） Wherein, ； ； ； ； ； wherein, is a decision variable; denotes an augmented coefficient vector; is a node admittance matrix; is a node and generator set adjacency matrix; is a branch admittance matrix; is an upper limit of power transmission allowed by a transmission line; is an active load of the power system; are minimum and maximum values of active power allowed to be generated by a generator set, respectively; are minimum and maximum values of voltage phase angle.

6. The method of claim 5, wherein: In step S13), by introducing translation variables and slack variables equivalent transformation of equation (4) into a standard linear programming problem; that is: （5） Wherein, ； wherein, is a diagonal matrix, is a constraint number; is a variable number.

7. The method of claim 6, wherein the method is based on quasi- interior point embedding and mixed precision for power system DC optimal power flow evaluation. Solving the quasi- interior point embedding system to obtain an optimal solution; specifically as follows: At any point , the expansion into a power series form: wherein is the order of the power series; are the coefficients of the terms corresponding to the coefficients of the terms is the number of constraints; is the number of variables; Substitute equation (7) into equation (6) and compare the coefficients of the terms on both sides to obtain the power series unknown coefficients satisfied linear equations For the block structure of the coefficient matrix, the solution of the above linear equation group is calculated by simplifying and using a mixed precision method: first, initial decomposition is performed under single precision, and then iteration improvement is performed using double precision; while maintaining the accuracy of the high-precision solution, the linear equation group is solved at a high speed; According to the power series expansion of , a rational approximation function is constructed to expand the convergence domain. Then, the parameter value of that satisfies equation (6) with an error less than a given tolerance and close to is found. Take as the new starting point, let , and repeat the above steps until .

8. The method of claim 7, wherein the method is based on quasi- interior point embedding and mixed precision for power system DC optimal power flow evaluation. In step S3), the optimal solution is obtained by solving the quasi- interior point embedding system based on the fast flexible holomorphic embedding and mixed precision, specifically comprising the following steps: S31)setting the maximum order of the power series expansion as , the allowable error as , the initial continuation interval as , the minimum threshold value of the continuation interval as , the reduction ratio as , the initial iteration point as , the continuation initial point as , the continuation end point as ; S32), introducing parameters , constructing quasi-interior point embedding system: （6） S33), and At the point is expressed as a power series expansion: ​ S34), substituting the power series expansion of into the quasi- interior point embedding system, to obtain an equation with the power series expansion coefficients as unknowns: ； ； S35) when , , , ; S36) when the equation satisfied by the coefficients of the power series expansion is a linear system of equations, denoted by: ​ （9） wherein denotes the coefficient matrix; denotes the power series expansion coefficients to be solved; denotes the right-hand side term; , , denote vectors composed of the power series expansion coefficients, respectively; , is a diagonal matrix whose diagonal elements are , , is the identity matrix; When time, ; When time, ; wherein is a diagonal matrix whose diagonal elements are ; S37), for the block structure of the coefficient matrix the linear equation system (9) is simplified to: （10b） （10c） wherein is a symmetric positive definite matrix; S38)、use mixed precision technology to solve linear equations (10a) to get , and then use double precision calculation (10b), (10c) to get , while maintaining high-precision solution accuracy, while accelerating the solution; S39) constructing a rational approximation function to enlarge the convergence domain by using the obtained power series expansion coefficients , constructing a rational approximation function to enlarge the convergence domain by using the obtained power series expansion coefficients S40) Determine when When, the equation Is the maximum error at both ends less than the allowable error? If satisfied, proceed to step S41; otherwise, narrow the interval. until the condition is met; S41), let S33) to S40) are repeated until .

9. The method of claim 8, wherein: In step S38), specifically comprising the following steps: S381), Calculate the matrix The initial solution is obtained by back-substituting the LU decomposition in single-precision mode. ; S382), calculate the residual with double precision i.e.: S383), using the LU decomposition of step S381), compute , obtaining the modified direction ; S384), updating ; S385), repeat steps S382) - S384); until a maximum number of iterations is reached or an accuracy requirement is met, output the solution ; S386), double precision calculation , , resulting in .

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