Electric power system direct current optimal power flow evaluation method based on quasi-interior point embedding and mixing precision

Abstract

The invention provides a power system DC optimal power flow evaluation method based on quasi-interior point embedding and mixing precision, and the method comprises the steps: obtaining power grid data, and building a DC optimal power flow calculation model; constructing a simulated interior point embedding system; solving the quasi-interior point embedding system based on rapid and flexible full-pure embedding and mixed precision to obtain an optimal solution; and evaluating a direct-current optimal power flow scheduling scheme according to the optimal solution. According to the method, a quasi-interior-point embedding system is constructed based on the idea that an interior-point method controls iteration points to be close to a constraint boundary and an optimal solution along a central path, an initial value can be flexibly selected, and meanwhile, the quasi-interior-point embedding system is constructed by referring to the characteristic that the central path of the interior-point method is always in a feasible region so as to guarantee that the optimal feasible solution is finally obtained; by adopting segmented low-order approximation, the calculation efficiency is effectively improved; the mixed precision technology is adopted to solve the linear equation set, calculation time and resource consumption are reduced on the premise that the precision and stability of the solution are guaranteed, and a more efficient and accurate optimization scheduling scheme is provided.

Description

Technical Field

[0001] The present invention relates to the technical field of power system planning, dispatching, operation and maintenance, and in particular to a method for evaluating the direct current optimal power flow of a power system based on quasi-inner point embedding and mixed precision. Background Art

[0002] As one of the basic problems in the optimal dispatching of a power system, the core research content of the Optimal Power Flow (OPF) problem is to optimize the dispatching operation of the power system, reduce the energy loss of the system, and obtain a power flow distribution with lower generation cost under the condition of ensuring the safe and stable operation of the system. The optimal power flow is a typical non-convex optimization problem, and its solution task is an NP-hard problem, which cannot guarantee global convergence or guarantee to complete the calculation within polynomial time. In order to improve the calculation efficiency and enhance the convergence, the non-linear alternating current optimal power flow is usually approximated by the linearized direct current optimal power flow (DC Optimal Power Flow, DC-OPF) problem. The DC-OPF model approximately describes the non-linear characteristics in the power system, assumes that the voltage amplitude remains constant, and ignores the influence of reactive power.

[0003] With the expansion of the scale of the power system, the number of nodes and lines in the power grid increases exponentially. The bottlenecks of a class of DC-OPF solution methods (such as the interior point method) based on traditional iterative ideas gradually appear in terms of calculation efficiency and resource consumption: the interior point method is sensitive to the selection of the initial point. If the initial point is not selected properly, it may cause the algorithm to be difficult to converge; at the same time, in actual calculations, it has a high dependence on the iteration step size and requires multiple calculations and adjustments to find the optimal solution, so the calculation efficiency is low and it is not conducive to solving complex examples. Another type is the holomorphic embedding method based on non-iterative ideas. Its main steps include constructing a suitable embedding system according to the target problem, obtaining the series expansion of the solution function of the embedding system, and calculating high-quality approximate values through the series expansion. A large number of numerical experiments show that the holomorphic embedding method is more robust and effective than the classical iterative method when solving the power flow problem.

[0004] Although the holomorphic embedding method can provide a relatively accurate solution process in theory, in actual calculations, it is necessary to construct a suitable embedding system according to the target problem, and in order to meet the accuracy requirements, it is necessary to continuously calculate the high-order terms in the series expansion, which directly affects the convergence, stability and calculation efficiency of the method. If the embedding system is constructed improperly or the order of the expansion coefficients calculated is too high, problems such as numerical instability, slow convergence speed, and low calculation efficiency may occur, resulting in the system being unable to make optimization decisions in time, thus affecting the safety and real-time performance of power grid dispatching. Summary of the Invention

[0005] Aiming at the deficiencies of the existing technology, the present invention provides a method for evaluating the direct current optimal power flow of a power system based on quasi-inner point embedding and mixed precision. The present invention processes the DC-OPF problem through steps such as constructing a quasi-inner point embedding system, piecewise rational approximation, and mixed precision acceleration, combining efficient numerical calculation methods with modern hardware acceleration technology, providing strong support for the real-time performance and accuracy of large-scale power system optimal dispatching; moreover, the present invention has the advantages of faster calculation speed, better convergence, and stronger robustness, and can better meet the requirements of new power system planning and dispatching.

[0006] The technical solution of the present invention is as follows: A method for evaluating the direct current optimal power flow of a power system based on quasi-inner point embedding and mixed precision, comprising the following steps:

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

[0008] S2), Construct a quasi-inner point embedding system based on the direct current optimal power flow calculation model;

[0009] S3), Solve the quasi-inner point embedding system based on fast and flexible holomorphic embedding and mixed precision to obtain the optimal solution;

[0010] S4), Evaluate the direct current optimal power flow dispatching plan according to the optimal solution.

[0011] Preferably, in step S1), establishing a direct current optimal power flow calculation model specifically includes the following steps:

[0012] S11), Obtain power grid data and determine the objective function according to the power generation cost data of the generating units;

[0013] S12), Determine the constraint set according to the power grid data;

[0014] S13), Establish a direct current optimal power flow calculation model according to the objective function and the constraint set.

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

[0016]

[0017] Among them, is the voltage phase angle of each node; is the active power of the generating unit, n b is the number of nodes, n g is the number of generating units; is the cost function, is the active power output of generating unit i, c i is the first-order coefficient of the cost function of generating unit i; c initis the set of first-order term coefficients of the cost function of the generator set; represents the augmented coefficient vector; is the decision variable.

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

[0019] Preferably, in step S12), the equality constraints of the DC optimal power flow problem are determined by the nodal power balance equation, that is:

[0020] B bus Θ + P d -C g P g = 0 (2);

[0021] In the formula, B bus is the nodal admittance matrix; is the voltage phase angle of each node; P d is the active power load of the power system, C g is the adjacency matrix of the node and the generator set: when the generator set j is connected to the node i, the element in the i-th row and j-th column of the adjacency matrix C g takes the value of 1, otherwise it takes the value of 0; P g is the active power of the generator set.

[0022] Preferably, in step S12), the inequality constraint set of the DC optimal 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]

[0024] -F max ≤ B f Θ ≤ F max ;

[0025] In the formula, are respectively the minimum and maximum values of the active power that the generator set is allowed to generate; B f is the branch admittance matrix; F max is the upper limit of the power that the transmission line is allowed to transmit.

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

[0027]

[0028] where,

[0029]

[0030] ​

[0031]

[0032]

[0033]

[0034] Among them, since the DC-OPF model assumes that the voltage phase angle difference is very small and the voltage phase angle of the reference node is 0, Θ can be set. min , Θ max are the minimum and maximum values of the voltage phase angle Θ.

[0035] Preferably, in step S13), by introducing the translation variable and the slack variable w + ≥0, w - ≥0, the above problem is equivalently transformed into a standard linear programming problem; that is:

[0036]

[0037] Among them,

[0038]

[0039] Among them, I is a diagonal matrix, m is the number of constraints; n is the number of variables.

[0040] Preferably, in step S2), a quasi-interior point embedding system is constructed based on the DC optimal power flow calculation model, including the following steps:

[0041] S21), Let be the dual variable of x, and introduce the parameter α ∈ [α 0 , α 1 ;

[0042] S22), For any initial point x (0) , s (0) ≥0, x (0) , s (0) , y (0) ; Design the quasi-interior point embedding system as follows:

[0043]

[0044] In the formula, A = (a ij ) m×n is the coefficient matrix; ζ (0) = Ax (0) - b, respectively represent vector functions with the embedding parameter α; X(α), X (0) is a diagonal matrix, and its diagonal elements are respectively x i (α),

[0045] S23) When α = α 0 , take x(α 0 ) = x (0) , s(α 0 ) = s (0) , y(α 0 ) = y (0) ; As α gradually approaches α 0 from α 1 , the values of x(α), s(α), y(α) give a homotopy path that gradually approaches the solution of the original problem; When α = α 1 , x(α 1 ), s(α 1 ), y(α 1 ) are what we want.

[0046] Preferably, in step S3), the optimal solution is obtained by solving the quasi - interior - point embedding system based on fast and flexible holomorphic embedding and mixed precision, as follows:

[0047] At any point α # of α, expand x(α), s(α), y(α) in the form of power series:

[0048]

[0049]

[0050] In the formula, q is the order of the power series; ξ i,q , η i,q , γ k,q are respectively the coefficients of x i (α), s i (α), y k (α) corresponding to the (α - α # ) q term;

[0051] Substitute equation (7) into equation (6), and compare the coefficients of the (α - α # ) q term on both sides of the equation to obtain the linear equations satisfied by the unknown coefficients ξ i,q , η i,q , γ i,q ;

[0052] For the block structure of the coefficient matrix, after simplification, the solution of the above linear equations is calculated using the mixed-precision method: first, perform the initial decomposition in single precision, and then use double precision for iterative improvement; while maintaining the accuracy of the high-precision solution, accelerate the solution of the linear equations;

[0053] Then, according to the obtained power series expansions of x i (α), s i (α), y k (α), construct a rational approximation function to expand the convergence domain; then, find the parameter value in the solution path that satisfies the error in Equation (6) is less than the given allowable error and is close to α 1 ; Take as the new starting point, and let Repeat the above steps until α # ≥α 1 .

[0054] Preferably, in step S3), based on the fast and flexible holomorphic embedding and mixed-precision solution of the quasi-interior point embedding system, the optimal solution is obtained, which specifically includes the following steps:

[0055] S31) Set the maximum order of the power series expansion to q max , the allowable error to ∈ > 0, the initial continuation interval Δα ibt > 0, the minimum threshold of the continuation interval Δ min , the reduction ratio the initial iteration point

[0056] x (0) , s (0) , y (0) , the continuation initial point α # = α 0 = 0, the continuation end point α 1 = 1;

[0057] S32) Introduce the parameter α and construct a quasi-interior point embedding system:

[0058]

[0059] S33) Let Δα = Δα int , and at the point α # , express x i (α), s i (α), y k (α) as a power series expansion: x i (α) = Σ q≥0 ξ i,q (α - α # ) q , 1 ≤ i ≤ n

[0060] s i (α) = Σ q≥0 η i,q (α - α # ) q , 1 ≤ i ≤ n (7)

[0061] y k (α) = Σ q≥0 γ k,q (α - α # ) q , 1 ≤ k ≤ m

[0062] S34) Substitute the power - series expansion of x i (α), s i (α), y k (α) into the quasi - interior - point embedding system to obtain an equation with the coefficients of the power - series expansion as unknowns:

[0063]

[0064] S35) When q = 0, ξ i,q = x i (α # ), η i,q = s i (α # ), γ k,q = y k (α # );

[0065] S36) When q ≥ 1, the equations satisfied by the coefficients ξ i,q , η i,q , γ k,q of the power - series expansion are linear equations and can be expressed as:

[0066] A q λ q = B q (9)

[0067] Among them, represents the coefficient matrix; represents the coefficients of the power - series expansion to be solved; represents the right - hand side term; respectively represent the vectors composed of the coefficients of the power - series expansion; X 0 , S 0 are diagonal matrices, and their diagonal elements are ξ i,0 , η i,0 (1 ≤ i ≤ n), and I is the identity matrix;

[0068] When q = 1,

[0069] When \(q\geq2\),

[0070] where, \(\Xi\) r is a diagonal matrix, and its diagonal elements are \(\xi\) i,r (\(1\leq i\leq n\));

[0071] S37) For the block structure of the coefficient matrix \(A\) q , the linear equation (9) is simplified to:

[0072]

[0073]

[0074] \(\xi\) q = \(S\) 0 -1 (\(B\) ξq - \(X\) 0 \(\eta\) q ) (10c)

[0075] where, is a symmetric positive definite matrix;

[0076] S38) Solve the linear equation (10a) using the mixed - precision technique to obtain \(\gamma\) q , and then use double - precision to calculate (10b) and (10c) to obtain \(\eta\) q , \(\xi\) q , achieving accelerated solution while maintaining the accuracy of the high - precision solution;

[0077] S39) Through the already obtained coefficients \(\xi\) i,q , \(\eta\) i,q , \(\gamma\) k,q (\(1\leq q\leq q\) max ), construct a rational approximation function to expand the convergence domain;

[0078] S40) Judge whether the maximum error between the two ends of equation (6) is less than the tolerance \(\epsilon\) when \(\alpha\in[\alpha\) # , \(\alpha\) # +\(\Delta\alpha]\). If satisfied, go to step S41); if not satisfied, shrink the interval \(\Delta\alpha\) until the condition is met;

[0079] S41) Let \(\alpha\) # ←\(\alpha\) # +\(\Delta\alpha\), repeat S33) to S40) until \(\alpha\) # \(\geq\alpha\) 1 .

[0080] Preferably, in step S38), it specifically includes the following steps:

[0081] S381), Calculate the matrix Perform LU decomposition in single precision and perform back substitution to obtain the initial solution

[0082] S382), Calculate the residual r in double precision, i.e.:

[0083]

[0084] In the formula,

[0085] S383), Utilize the LU decomposition in step S381) to calculate to obtain the correction direction d;

[0086] S384), Update

[0087] S385), Repeat steps S382)-S384); until the maximum number of iterations is reached or the accuracy requirement is met, output the solution

[0088] S386), Calculate in double precision ξ q = S 0 -1 (B ξq - X 0 η q ), and finally obtain ξ q , η q , γ q .

[0089] Preferably, in step S4), according to the value of the rational approximation of the last series expansion at α # = α 1 to obtain x * , 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 Θ * of each node and the optimal active power of the generator

[0090] The beneficial effects of the present invention are as follows:

[0091] 1. Based on the idea of the interior point method to control the iteration point to approach the constraint boundary and the optimal solution along the central path, the present invention constructs a quasi-interior point embedding system, which can flexibly select the initial value; at the same time, drawing on the characteristic that the central path of the interior point method is always within the feasible region, a quasi-interior point embedding system is constructed to ensure that it finally obtains the optimal feasible solution, significantly reducing the infeasible solutions caused by using other embedding systems;

[0092] 2. The present invention adopts piecewise low-order approximation, avoiding problems such as numerical instability and large computational amount that occur in the traditional holomorphic embedding method when calculating high-order terms of series expansion, and effectively improving the computational efficiency.

[0093] 3. The present invention uses the mixed-precision technology to solve the linear equations, accelerating the calculation process on the premise of ensuring the accuracy and stability of the solution, reducing the calculation time and resource consumption, so as to provide a more efficient and accurate optimal scheduling scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 is the framework flowchart of the method of the present invention;

[0095] Figure 2 is the schematic flowchart of the fast and flexible holomorphic embedding based on quasi-inner point embedding and mixed precision of the present invention;

[0096] Figure 3 is the flowchart of calculating the linear equations by mixed precision of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0097] The following further describes the specific embodiments of the present invention with reference to the drawings:

[0098] As Figure 1 shown, this embodiment provides a method for evaluating the direct current optimal power flow of a power system based on quasi-inner point embedding and mixed precision, including the following steps:

[0099] S1). Obtain grid data and establish a direct current optimal power flow calculation model; specifically including the following steps:

[0100] S11). Obtain grid data and determine the objective function according to the power generation cost data of the generating units; the optimal power flow problem is to optimize the adjustable factors such as the output power of each generating unit and the voltage of each node in the power system, and find the optimal power flow distribution to make the total power generation cost of the system the most economical; the expression of the objective function is:

[0101]

[0102] Wherein, is the voltage phase angle of each node; is the active power of the generating unit, n b is the number of nodes, n g is the number of generating units; is the cost function, is the active power output of generating unit i, c i is the first-order coefficient of the cost function of generating unit i; c init is the set of first-order coefficients of the cost functions of the generating units; represents the augmented coefficient vector; is a decision variable.

[0103] The decision variable mentioned above The set c of the first-order term coefficients of the cost function of the generator set init , the active power P of the generator set g , the augmented coefficient vector are respectively expressed as:

[0104]

[0105] In the formula, represents an n b dimensional zero vector.

[0106] S12), determine the constraint set according to the power grid data;

[0107] In this embodiment, the constraint set includes equality constraints and inequality constraints. Among them, the equality constraints of the DC optimal power flow problem are determined by the nodal power balance equation, that is:

[0108] B bus Θ + P d - C g P g = 0 (2);

[0109] In the formula, B bus is the nodal admittance matrix; is the voltage phase angle of each node; P d is the active power load of the power system, C g is the adjacency matrix of nodes and generator sets: when the generator set j is connected to the node i, the element g in the i-th row and j-th column of the adjacency matrix C takes the value of 1, otherwise it takes the value of 0; is the active power of the generator set.

[0110] The inequality constraint set of the DC optimal power flow problem is determined by the output limit of the generator set and the transmission power limit of the transmission line; that is:

[0111]

[0112] - F max ≤ B f Θ ≤ F max ;

[0113] In the formula, is the voltage phase angle of each node; are respectively the minimum and maximum values of the active power that the generator set is allowed to generate; B f is the branch admittance matrix; F maxIt is the upper limit of the power that the transmission line is allowed to transmit.

[0114] S13), Establish a DC optimal power flow calculation model according to the objective function and the constraint set. In this embodiment, the expression of the DC optimal power flow calculation model is:

[0115]

[0116] Wherein,

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] Wherein, since the DC-OPF model assumes that the voltage phase angle difference is very small and the voltage phase angle of the reference node is 0, Θ min , Θ max are the minimum and maximum values of the voltage phase angle.

[0123] In addition, in this embodiment, by introducing the translation variable and the slack variable w + ≥0, w - ≥0, the above problem is equivalently transformed into a standard linear programming problem; that is:

[0124]

[0125] Wherein,

[0126]

[0127] Wherein, I is a diagonal matrix, m is the number of constraints; n is the number of variables.

[0128] S2), Construct a quasi-interior point embedding system based on the DC optimal power flow calculation model; specifically, it includes the following steps:

[0129] S21), Let be the dual variable of x, and introduce the parameter α ∈ [α 0 , α 1 ;

[0130] S22), For any initial point x (0) , s (0) ≥0, x (0) , s (0),y (0) ; Design the quasi - interior - point embedding system as follows:

[0131]

[0132] In the formula, \(A=(a ij ) m×n is the coefficient matrix; \(\zeta (0) = Ax (0) -b, respectively represent vector functions with the embedding parameter \(\alpha\) as the variable; \(X(\alpha)\), \(X (0) is a diagonal matrix, and its diagonal elements are respectively \(x i (\alpha)\),

[0133] S23) When \(\alpha=\alpha 0 , take \(x(\alpha 0 ) = x (0) , s(\alpha 0 ) = s (0) , u(\alpha 0 ) = y (0) ; As \(\alpha\) gradually approaches \(\alpha 0 from \(\alpha 1 , the values of \(x(\alpha), s(\alpha), u(\alpha)\) give a homotopy path that gradually approaches the solution of the original problem; when \(\alpha=\alpha 1 , \(x(\alpha 1 ), s(\alpha 1 ), y(\alpha 1 ) are what we want.

[0134] S3) Based on the fast and flexible holomorphic embedding and mixed - precision solution of the quasi - interior - point embedding system to obtain the optimal solution; specifically as follows:

[0135] At any point \(\alpha # of \(\alpha\), expand \(x(\alpha), s(\alpha), y(\alpha)\) in the form of a power series:

[0136]

[0137] In the formula, \(q\) is the order of the power series; \(\xi i,q , \(\eta i,q , \(\gamma k,q are the coefficients corresponding to the terms of \(x i (\alpha), s i (\alpha), y k (\alpha)\) corresponding to \((\alpha-\alpha # ) q ;

[0138] Substitute equation (7) into equation (6), and compare the left - hand and right - hand sides of the equation for \((\alpha-\alpha # )q The coefficients of the terms are used to obtain the unknown coefficients ξ of the power series i,q , η i,q , γ i,q for the linear equations they satisfy;

[0139] For the block structure of the coefficient matrix, after simplification, the solution of the above linear equations is calculated using the mixed-precision method: first, perform an initial decomposition in single precision, and then use double precision for iterative improvement; while maintaining the accuracy of the high-precision solution, accelerate the solution of the linear equations;

[0140] Then, according to the power series expansions of x i (α), s i (α), y k (α) obtained, construct a rational approximation function to expand the convergence domain; then, find the parameter value in the solution path that satisfies the error in Equation (6) less than the given allowable error and is close to α 1 Take as the new starting point, and let Repeat the above steps until α # ≥ α 1 .

[0141] As Figure 2 shown, this embodiment obtains the optimal solution based on the fast and flexible holomorphic embedding and the mixed-precision solution of the quasi-interior-point embedding system, which specifically includes the following steps:

[0142] S31), Set the maximum order of the power series expansion to q max , the allowable error to ∈ > 0, the initial continuation interval Δα ibt > 0, the minimum threshold Δ of the continuation interval min , the reduction ratio the initial iteration point

[0143] x (0) , s (0) , y (0) , the continuation initial point α # = α 0 = 0, the continuation end point α 1 = 1;

[0144] S32), Introduce the parameter α and construct a quasi-interior-point embedding system:

[0145]

[0146] S33), Let Δα = Δα int , at the point α # x i (α), s i (α), y​k (α) is expressed as a power series expansion: x i (α) = Σ q≥0 ξ i,q (α - α # ) q , 1 ≤ i ≤ n

[0147] s i (α) = Σ q≥0 η i,q (α - α # ) q , 1 ≤ i ≤ n (7)

[0148] y k (α) = Σ q≥0 γ k,q (α - α # ) q , 1 ≤ k ≤ m

[0149] S34), Substitute the power series expansions of x i (α), s i (α), y k (α) into the quasi-interior point embedding system to obtain an equation with the coefficients of the power series expansion as unknowns:

[0150]

[0151] S35), When q = 0, ξ i,q = x i (α # ), η i,q = s i (α # ), γ k,q = y k (α # );

[0152] S36), When q ≥ 1, the equations satisfied by the coefficients ξ i,q , η i,q , γ k,q of the power series expansion are linear equations and can be expressed as:

[0153] A q λ q = B q (9)

[0154] Where, represents the coefficient matrix; represents the variable to be solved; represents the right-hand side term; respectively represent the vectors composed of the coefficients of the power series expansion; X 0 、S0 is a diagonal matrix, and its diagonal elements are ξ i,0 and η i,0 (1 ≤ i ≤ n), and I is the identity matrix.

[0155] When q = 1, B ξ,q = -X (0) s (0) , B γ,q = -ζ (0) ,

[0156] When q ≥ 2, B γ,q = 0, B η,q = 0;

[0157] Among them, Ξ r is a diagonal matrix, and its diagonal elements are ξ i,r (1 ≤ i ≤ n);

[0158] S37), for the block structure of the coefficient matrix A q , the linear equation (9) is simplified to:

[0159]

[0160]

[0161] ξ q = S 0 -1 (B ξq - X 0 η q ) (10c)

[0162] Among them, is a symmetric positive definite matrix;

[0163] S38), solve the linear equation (10a) using the mixed-precision technology to obtain γ q , and then use double-precision to calculate (10b) and (10c) to obtain η q , ξ q , and accelerate the solution while maintaining the accuracy of the high-precision solution; as Figure 3 shown, it specifically includes the following steps:

[0164] S381), calculate the LU decomposition of the matrix in single precision, and perform backward substitution to obtain the initial solution

[0165] S382), calculate the residual r using double precision, that is:

[0166]

[0167] S383), calculate using the LU decomposition in step S381) to obtain the correction direction d;

[0168] S384), update

[0169] S385), repeat steps S382)-S384); until the maximum number of iterations is reached or the accuracy requirement is met, output the solution

[0170] S386), calculate with double precision ξ q = S 0 -1 (B ξq - X 0 η q ), and finally obtain ξ q , η q , γ q .

[0171] S39), through the coefficients ξ i,q , η i,q , γ k,q (1 ≤ q ≤ q max ) of the obtained power series expansion, construct a rational approximation function to expand the convergence domain;

[0172] S40), determine whether the maximum error between both ends of equation (6) is less than the allowable error ∈ when α ∈ [α # , α # + Δα]. If satisfied, go to step S41); if not satisfied, shrink the interval Δα until the condition is met; specifically as follows:

[0173] If Δα > Δ min , let Repeat S40);

[0174] If Δα ≤ Δ min , exit the loop, calculation fails.

[0175] S41), let α # ← α # + Δα, repeat S33) to S40) until α # ≥ α 1 .

[0176] S4), evaluate the DC optimal power flow scheduling scheme according to the optimal solution;

[0177] In this embodiment, according to the rational approximation of the last power series expansion at α # = α 1The value at obtains x * , that is, the optimal solution of the DC optimal power flow problem, so as to obtain the DC optimal power flow scheduling plan, including the optimal voltage phase angle Θ of each node * and the optimal active power of the generator

[0178] The above embodiments and descriptions in the specification only illustrate the principles and the best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed.

Claims

1. A DC optimal power flow evaluation method for power systems based on quasi-interior point embedding and mixed precision, characterized in that: The steps include: S1), obtain power grid data and establish a DC optimal power flow calculation model; S2), constructing a quasi-interior point embedding system based on the DC optimal power flow calculation model; S3) Solve the quasi-interior point embedding system based on fast and flexible holomorphic embedding and mixed precision to obtain the optimal solution; S4), evaluating the DC optimal power flow dispatching scheme according to the optimal solution; According to the rational approximation of the last series expansion, # = the value at α1 to get x * , that is, the optimal solution of the DC optimal power flow problem, thus obtaining the DC optimal power flow scheduling scheme, including the optimal voltage phase angle Θ of each node * and the optimal active power of the generator 2. The method for evaluating DC optimal power flow in a power system based on quasi-interior point embedding and mixed precision according to claim 1 is characterized in that: In step S1), a DC optimal power flow calculation model is established, which specifically includes the following steps: S11), obtaining power grid data, and determining the objective function according to the power generation cost data of the generator set; S12), determining a constraint set according to power grid data; S13), establishing a DC optimal power flow calculation model according to the objective function and the constraint set.

3. The method for evaluating DC optimal power flow in a power system based on quasi-interior point embedding and mixed precision according to claim 2 is characterized in that: In step S11), the expression of the objective function is: in, is the voltage phase angle of each node; is the active power of the generator set, n b is the number of nodes, n g is the number of generator sets; is the cost function, is the active output of generator set i, c i is the first-order coefficient of the cost function of generator set i; c init is the set of first-order coefficients of the cost function of the generator set; represents the augmentation coefficient vector; is the decision variable; T represents the transposition operation.

4. The method for evaluating DC optimal power flow in a power system based on quasi-interior point embedding and mixed precision according to claim 3 is characterized in that: In step S12), the constraint set includes equality constraints and inequality constraints; wherein, The equality constraints of the DC optimal power flow problem are determined by the node power balance equation, namely: B bus Θ+P d -C g P.S g 00 (2) In the formula, B bus is the node admittance matrix; is the voltage phase angle of each node; P d is the active load of the power system, C j is the adjacency matrix of nodes and generators: When generator j is connected to node i, the adjacency matrix C g The element in row i and column j of The value is 1, otherwise the value is 0; is the active power of the generator set; the inequality constraint set of the DC optimal power flow problem is determined by the output limit of the generator set and the transmission power limit of the transmission line; that is: -F max ≤B f Θ≤F max ; In the formula are the minimum and maximum values ​​of active power allowed to be generated by the generator set; B f is the branch admittance matrix; F max The upper limit of the power allowed to be transmitted by the transmission line.

5. The method for evaluating DC optimal power flow in a power system based on quasi-interior point embedding and mixed precision according to claim 4 is characterized in that: In step S13), the expression of the DC optimal power flow calculation model is: in, in, is the decision variable; represents the augmentation coefficient vector; B bus is the node admittance matrix; C g is the adjacency matrix of nodes and generators; B f is the branch admittance matrix; F max P is the upper limit of the power allowed to be transmitted by the transmission line; d is the active load of the power system; are the minimum and maximum values ​​of active power allowed to be generated by the generator set; Θ min ,Θ max To set the minimum and maximum values ​​of the voltage phase angle.

6. The method for evaluating DC optimal power flow in a power system based on quasi-interior point embedding and mixed precision according to claim 5 is characterized in that: In step S13), by introducing the translation variable and the slack variable w + ≥0,w - ≥0, the above problem is equivalently transformed into a standard linear programming problem; Right now: in, Where I is a diagonal matrix, m is the number of constraints; n is the number of variables.

7. The method for evaluating DC optimal power flow in a power system based on quasi-interior point embedding and mixed precision according to claim 6 is characterized in that: In step S2), a quasi-interior point embedding system is constructed based on the DC optimal power flow calculation model, including the following steps: S21) Set is the dual variable of x, and introduces parameter α∈[α0,α1]; S22), for any x (0) ,s (0) The initial point x ≥ 0 (0) ,s (0) ,y (0) ; Design the quasi-interior point embedding system as follows: In the formula, A=(a ij ) m×n is the coefficient matrix; ζ (0) =Ax (0) -b, They represent vector functions with the embedding parameter α as a variable; X(α), X (0) is a diagonal matrix whose diagonal elements are x i (α), S23), when α=α0, take x(α0)=x (0) ,s(α0)=s (0) ,y(α0)=y (0) ; As α gradually approaches α0 from α1, the values ​​of x(α), s(α), and y(α) give a homotopic path that gradually approaches the solution to the original problem; when α=α1, x(α1), s(α1), and y(α1) are what we want.

8. The method for evaluating DC optimal power flow in a power system based on quasi-interior point embedding and mixed precision according to claim 7 is characterized in that: In step S3), the optimal solution is obtained by solving the quasi-interior point embedding system based on fast and flexible holomorphic embedding and mixed precision, as follows: At any point α # At , expand x(α), s(α), u(α) into a power series form: Where q is the order of the power series; ξ i,q ,η i,q ,γ k,q x i (α),s i (α),y k (α) corresponds to (α-α # ) q The coefficient of the term; Substitute equation (7) into equation (6) and compare the left and right sides of the equation (α-α # ) q The coefficient of the term gives the unknown coefficient ξ of the power series i,q ,η i,q ,γ i,q The linear equations satisfied; The block structure of the coefficient matrix is ​​simplified and the solution of the above linear equations is calculated using a mixed precision method: the initial decomposition is first performed in single precision, and then iterative improvement is performed using double precision; the accelerated solution of the linear equations is achieved while maintaining the accuracy of the high-precision solution; According to the obtained x i (α),s i (α),y k The power series expansion of (α) is used to construct a rational approximation function to expand the convergence domain; then, the parameter value that satisfies equation (6) and is smaller than the given allowable error and close to α1 is found. Will As a new starting point, Repeat the above steps until α # ≥α1.

9. The method for evaluating DC optimal power flow in a power system based on quasi-interior point embedding and mixed precision according to claim 8, characterized in that: In step S3), the optimal solution is obtained by solving the quasi-interior point embedding system based on fast and flexible holomorphic embedding and mixed precision, which specifically includes the following steps: S31), set the maximum order of the power series expansion to q max , allowable error is ∈>0, initial extension interval Δα int >0, minimum threshold of extension interval Δ min , reduction ratio Initial iteration point x (0) ,s (0) ,y (0) , extend the initial point α # =α0=0, extension end point α1=1; S32), introduce parameter α and construct a quasi-interior point embedding system: S33), let Δα=Δα int , at point α # x i (α),s i (α),y k (α) is expressed as a power series expansion: S34) x i (α),s i (α),y k Substituting the power series expansion of (α) into the quasi-interior point embedding system, we obtain the equation with the coefficients of the power series expansion as unknowns: S35), when q = 0, ξ i,q = x i (α # ), η o,q = s o (α # ), γ l,q = y k (α # ); S36), when q≥1, the power series expansion coefficient ξ i,q ,η i,q ,γ k,q The equations satisfied are a system of linear equations, expressed as: A q l q =B q (9) in, represents the coefficient matrix; represents the coefficients of the power series expansion to be solved; Indicates the right-hand term; They represent vectors consisting of power series expansion coefficients; X0 and S0 are diagonal matrices, whose diagonal elements are ξ i,0 , η i,0 (1≤i≤n), I is the unit matrix; When q = 1, B ξ,q =-X (0) s (0) ,B γ,q =-ζ (0) ,B η,q =-ζ (0) ; When q≥2, B γ,q =0,B η,q =0; Among them, r is a diagonal matrix whose diagonal elements are ξ i,r (1≤i≤n); S37), for the coefficient matrix A q The block structure simplifies the linear equations (9) to: in, is a symmetric positive definite matrix; S38) Solve the linear equations (10a) using mixed precision technology to obtain γ q , and then use double precision calculation (10b), (10c) to get η q ,ξ q , while maintaining high-precision solution accuracy, it can achieve accelerated solution; S39), through the power series expansion coefficient ξ i,q ,η i,q ,γ k,q (1≤q≤q max ), construct a rational approximation function to expand the convergence domain; S40), judge when α∈[α # ,α # +Δα], whether the maximum error at both ends of equation (6) is less than the allowable error ∈, if it is satisfied, go to step S41); if not, reduce the interval Δα until the condition is met; S41), let α # ←α # +Δα, repeat S33) to S40) until α # ≥α1.

10. The method for evaluating DC optimal power flow in a power system based on quasi-interior point embedding and mixed precision according to claim 9, characterized in that: Step S38) specifically includes the following steps: S381), calculation matrix LU decomposition in single precision, back substitution to get the initial solution S382), calculate the residual r with double precision, that is: S383), using the LU decomposition of step S381), calculate Get the correction direction d; S384), Update S385), repeat steps S382)-S384); until the maximum number of iterations is reached or the accuracy requirement is met, output the solution S386), using double precision calculation ξ q =S0 -1 (B ξq -X0η q ), and finally get ξ q ,η q ,γ q .

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