CN113489014B - Quick and flexible full-pure embedded power system optimal power flow evaluation method - Google Patents

Quick and flexible full-pure embedded power system optimal power flow evaluation method Download PDF

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CN113489014B
CN113489014B CN202110812483.5A CN202110812483A CN113489014B CN 113489014 B CN113489014 B CN 113489014B CN 202110812483 A CN202110812483 A CN 202110812483A CN 113489014 B CN113489014 B CN 113489014B
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power flow
power
approximation
power system
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CN113489014A (en
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汪涛
谭伟鹏
张文
刘彦志
张佳敏
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Sun Yat Sen University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Abstract

The invention discloses a rapid and flexible full-pure embedded power system optimal power flow assessment method, which comprises the following steps: acquiring power grid data and establishing an optimal power flow calculation model; establishing a differential power system based on the optimal power flow calculation model and solving an approximation value of a stable balance point to obtain an approximation value of a local optimal solution; comparing the obtained approximate values of the plurality of local optimal solutions based on global search to obtain an approximate global optimal solution; and evaluating an optimal power flow scheduling scheme according to the approximate global optimal solution. The invention provides a rapid, flexible and fully-pure embedded method combined with a global search technology, which is used for rapidly and efficiently calculating the approximate value of the stable balance point of a corresponding differential power system obtained by conversion according to an optimization problem to obtain a local optimal solution corresponding to an optimal power flow problem, and solves the problem that the convergence speed of the traditional optimization method is low. The method for evaluating the optimal power flow of the fast and flexible full-pure embedded power system can be widely applied to the field of optimal power flow.

Description

Quick and flexible full-pure embedded power system optimal power flow evaluation method
Technical Field
The invention relates to the field of optimal power flow, in particular to a rapid and flexible full-pure embedded power system optimal power flow assessment method.
Background
The optimal power flow (Optimal Power Flow, OPF) refers to an optimization process of adjusting parameters of various control devices in the system from the viewpoint of optimizing operation of the power system, and achieving minimization of an objective function under the constraint of meeting normal power balance of nodes and various safety indexes. Because the optimal power flow is an analysis method which simultaneously considers the safety and the economy of the network, the optimal power flow is widely applied to the aspects of safe operation of a power system, economic dispatch, power grid planning, reliability analysis of a complex power system, economic control of transmission blockage and the like. The optimal power flow is a typical nonlinear optimization problem, and the complexity of the scale and constraint of a complex power system makes it difficult to solve the nonlinear optimization problem robustly and efficiently.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a rapid and flexible full-pure embedded power system optimal power flow evaluation method, which solves the defects of low convergence speed and irregular convergence domain of the traditional optimization method.
The first technical scheme adopted by the invention is as follows: a fast and flexible full-pure embedded power system optimal power flow assessment method comprises the following steps:
s1, acquiring power grid data and establishing an optimal power flow calculation model;
s2, establishing a differential power system based on the optimal power flow calculation model, and solving an approximation value of a stable balance point to obtain an approximation value of a local optimal solution;
s3, comparing the obtained approximate values of the plurality of local optimal solutions based on a global search technology to obtain an approximate global optimal solution;
and S4, evaluating an optimal power flow scheduling scheme according to the approximate global optimal solution.
Further, the step of acquiring power grid data and establishing an optimal power flow calculation model specifically includes:
s11, acquiring power grid data;
s12, determining an objective function according to the power generation cost data of the generator nodes;
s13, determining a constraint set according to power grid data;
and S14, establishing an optimal power flow calculation model according to the objective function and the constraint set.
Further, the step of determining a constraint set according to the grid data specifically includes:
s131, determining an equation constraint set E according to grid node data in the grid data;
s132, determining an inequality constraint set N according to line constraint data and line structure data in the power grid data;
s133, determining a frame constraint set B according to node power constraint data, bus voltage constraint data and bus reference angle data in the power grid data.
Further, the step of establishing a differential power system based on the optimal power flow calculation model and solving the approximation of the stable balance point to obtain the approximation of the local optimal solution specifically comprises the following steps:
s21, converting the optimal power flow problem into an equation constraint optimization problem according to an optimal power flow model, and establishing an equivalent differential power system;
s22, solving an approximation value of a stable balance point of the differential power system based on a piecewise rational approximation method to obtain an approximation value of a local optimal solution of the optimal power flow problem.
Further, the differential power system may be expressed as follows:
Figure BDA0003168746010000021
in the above formula, X is an optimization variable, s is an embedding variable, t is a time variable of the power system,
Figure BDA0003168746010000022
refers to the orthogonal projection of the gradient of the objective function onto the constraint plane tangent space.
Further, the step of solving the approximation value of the stable balance point of the differential power system based on the piecewise rational approximation method to obtain the approximation value of the local optimal solution of the optimal power flow problem specifically comprises the following steps:
s221, initializing parameters, and setting the order q of the power series partial sum max The allowable error threshold e on both sides of the equation, the final stop error threshold epsilon, find any feasible point as the initial point X 0 ＝X(0)；
S222, giving a power series part and X (S) of a solution function vector X with respect to time S;
s223, substituting the power series part and X (S) into a differential power system to obtain an equation taking the power series expansion coefficient as an unknown number;
s224, comparing the same power series of S in the step S223, calculating each power series coefficient of X (S), and constructing a piecewise rational approximation function according to the power series information;
s225, substituting the value of the piecewise rational approximation function at s=s' into the differential power system, i.e.
Figure BDA0003168746010000023
Comparing whether the modulus of the difference between the left side and the right side of the equation is smaller than a preset threshold e to judge whether the power series converges at s';
s226, if the modulus of the difference between the left side and the right side of the equation is smaller than a preset threshold value e, expanding S 'and returning to the step S225, and finding S' which is as large as possible and meets the condition;
s227, if the modulus of the difference between the left side and the right side of the equation is not smaller than a preset threshold e, shrinking S' and returning to the step S225 until the modulus of the difference between the left side and the right side of the equation is smaller than the preset threshold e;
s228, taking X (S') as a new starting point X 0 ；
S229, looping steps S223-S228, calculating a solution function X (S) and a constant S represented by a piecewise rational approximation function * Wherein s is * So that
Figure BDA0003168746010000031
Hold, within the tolerance range +.>
Figure BDA0003168746010000032
Obtaining an approximation of the stable equilibrium point X (s * )；
S2210, approximation of stable equilibrium point X (S * ) The approximate value of the local optimal solution of the optimal power flow problem is obtained.
Further, the expression of the power series part of the solution function vector X with respect to time s and X(s) is as follows:
Figure BDA0003168746010000033
in the above, X k (s) represents the kth component of the power series part and vector X(s), X k [i]Representing the power series part and the i-th coefficient of the kth component of the vector X(s) with respect to the variable s.
Further, the step of comparing the obtained approximation values of the plurality of local optimal solutions based on the global search technology to obtain an approximate global optimal solution specifically includes:
s31, circulating the step S2 until the preset times are reached, and obtaining a plurality of local optimal solutions;
s32, comparing the plurality of local optimal solutions, and selecting the smallest local optimal solution as an approximate global optimal solution.
The method has the beneficial effects that: according to the method, the optimal power flow problem is converted into an initial value problem for solving the ordinary differential equation, the stable balance point of the corresponding differential power system is calculated rapidly and efficiently by combining a rapid and flexible full-pure embedded method of the global search technology, and the approximate global optimal solution corresponding to the optimal power flow problem is found, so that the power grid dispatching is optimized.
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FIG. 1 is a schematic diagram of providing grid optimal power flow for a dispatch center according to an embodiment of the present invention;
fig. 2 is a schematic illustration of an embodiment of the present invention.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples. The step numbers in the following embodiments are set for convenience of illustration only, and the order between the steps is not limited in any way, and the execution order of the steps in the embodiments may be adaptively adjusted according to the understanding of those skilled in the art.
The invention is a quick and flexible full-pure embedded method (FFHE) combined with a global search technology, and the stable balance point of a differential power system, namely a local optimal solution corresponding to the optimal power flow problem, is calculated quickly and efficiently, so that the defects of low convergence speed and irregular convergence domain of the traditional optimization method are overcome; meanwhile, the method solves the defects that the inverse of a function matrix cannot be solved, the calculated amount is large, the time consumption is long, the storage space is large and the like in the process of solving the differential power system by the conventional ordinary differential equation solving method.
Referring to fig. 1 and 2, the invention provides a fast and flexible full-pure embedded power system optimal power flow assessment method, which comprises the following steps:
s1, acquiring power grid data and establishing an optimal power flow calculation model;
s2, establishing a differential power system based on the optimal power flow calculation model, and solving an approximation value of a stable balance point to obtain an approximation value of a local optimal solution;
s3, comparing the obtained approximate values of the plurality of local optimal solutions based on a global search technology to obtain an approximate global optimal solution;
and S4, evaluating an optimal power flow scheduling scheme according to the approximate global optimal solution.
Further as a preferred embodiment of the method, the step of obtaining the grid data and establishing the optimal power flow calculation model specifically includes:
s11, acquiring power grid data;
s12, determining an objective function according to the power generation cost data of the generator nodes;
s13, determining a constraint set according to power grid data;
and S14, establishing an optimal power flow calculation model according to the objective function and the constraint set.
Specifically, the optimization vector x of the optimal power flow problem is generally defined by n b * 1-dimensional voltage amplitude V m And angle theta, n g * Active power P of 1-dimensional generator g And reactive power Q g Composition is prepared.
Figure BDA0003168746010000041
While the objective function we need to optimize is f (x) a single polynomial or other nonlinear cost function of the active and reactive power of each generator
Figure BDA0003168746010000042
And->
Figure BDA0003168746010000043
And: />
Figure BDA0003168746010000044
Figure BDA0003168746010000045
Is the active power corresponding to the ith generator +.>
Figure BDA0003168746010000046
And reactive power->
Figure BDA0003168746010000047
Or other non-linear cost function.
Further as a preferred embodiment of the method, the step of determining the constraint set according to the grid data specifically includes:
s131, determining an equation constraint set E according to grid node data in the grid data;
s132, determining an inequality constraint set N according to line constraint data and line structure data in the power grid data;
s133, determining a frame constraint set B according to node power constraint data, bus voltage constraint data and bus reference angle data in the power grid data.
Specifically, the set of equation constraints E is defined by 2*n b The nonlinear active power and reactive power balance equation consists of:
g P (θ,V m ,P g )＝0
g Q (θ,V m ,Q g )＝0
the inequality constraint set N is composed of two groups, each group N g The flow limit of each branch is composed of, usually, the voltage amplitude V m And a nonlinear function of angle θ, where h f Is the initial end value of each branch, h t Is the termination limit value of each branch:
h f (θ，V m )＝|F f (θ，V m )|-F max ≤0
h t (θ，V m )＝|F t (θ，V m )|-F max ≤0
wherein the flow rate F f Typically apparent power flow, but may also be active power flow or current, i.e.:
Figure BDA0003168746010000051
in addition, the reference angle theta of the bus is also provided, and the voltage amplitude V of the bus m Active power P g And reactive power Q g Is defined by the frame constraint set B:
Figure BDA0003168746010000052
Figure BDA0003168746010000053
Figure BDA0003168746010000054
Figure BDA0003168746010000055
further as a preferred embodiment of the method, the step of establishing a differential power system based on the optimal power flow calculation model and solving an approximation of a stable balance point to obtain an approximation of a locally optimal solution specifically includes:
s21, converting the optimal power flow problem into an equation constraint optimization problem according to an optimal power flow model, and establishing an equivalent differential power system;
specifically, the above optimal power flow problem can be described as follows:
minf(x)
S.t.g i (x)≤0i＝1，……，m
h j (x)＝0j＝1，……，l (1)
wherein the method comprises the steps of
Figure BDA0003168746010000056
Is an objective function g i (x) Represents the ith inequality constraint, h j (x) Representing the j-th equation constraint. We introduce m relaxation variables z i Corresponding to the m inequality constraints in the formula (1), respectively, will optimizeThe problem equivalence translates into:
minf(x)
S.t.g i (x)+z i 2 ＝0i＝1，……，m
h j (x)＝0j＝1，……，l (2)
the optimal power flow problem becomes an optimization problem with l+m equality constraints, and for convenience of the following expression, we will express the optimization problem of formula (2) as:
minf(X)
t.t.H(X)＝0 (3)
wherein H (X) is a function vector of dimension l+m, defining X to = [ X, z ]] T Let n=l+m, redefine f (X) as
Figure BDA0003168746010000061
Figure BDA0003168746010000062
Figure BDA0003168746010000063
Figure BDA0003168746010000064
And finally, establishing an equivalent differential power system:
Figure BDA0003168746010000065
in the above formula, X is an optimization variable, s is an embedding variable, t is a time variable of the power system,
Figure BDA0003168746010000066
refers to the orthogonal projection of the gradient of the objective function onto the constraint plane tangent space.
S22, solving an approximation value of a stable balance point of the differential power system based on a piecewise rational approximation method to obtain an approximation value of a local optimal solution of the optimal power flow problem.
First, for each component in the solution function vector X, we can develop it as a power series over time s:
Figure BDA0003168746010000067
X(0)＝X[0]＝X 0 (6)
where at s=0, the system is at an initial point.
The composite function formed by the solution function vector elementary operation can also be expanded into a power series with respect to the variable s:
Figure BDA0003168746010000068
Figure BDA0003168746010000069
wherein f [ i ]]，H[i]Is related to X k [i′]The method comprises the steps of carrying out a first treatment on the surface of the k=1, … …, n+m; i'. Ltoreq.i;
likewise DH can also be seen as related to X k [i′]Is a function of:
Figure BDA0003168746010000071
substituting the power series expansion of s in the formulas (6), (7) and (8) into the formula (5):
Figure BDA0003168746010000072
by comparing coefficients of the homonyms of the two sides of the formula (9) with respect to s, the coefficient with respect to the unknown number X can be determined k [i]The method comprises the steps of carrying out a first treatment on the surface of the k=1, … …, n+m; equation set with i.gtoreq.1.
X can be obtained after the above steps are completed k (s); k=1, …, n+m. According toAnd constructing a piecewise rational approximation function according to the existing power series information so as to enlarge the effective interval. Substituting the value of the piecewise rational approximation function at s=s' into equation (5), and comparing whether the modulus of the difference between the left and right sides of the equation is greater than a preset allowable threshold. As large s' as possible is found so that the modulus of the difference between the left and right sides of the equation is less than the threshold. Repeating the above steps with X (s') as a new starting point until s is found * So that
Figure BDA0003168746010000073
Less than the error limit given in advance, so we consider that an approximation of the stable equilibrium point is found.
Further as a preferred embodiment of the method, the step of solving the approximation value of the stable balance point of the differential power system based on the piecewise rational approximation method to obtain the approximation value of the local optimal solution of the optimal power flow problem specifically includes:
s221, initializing parameters, and setting the order q of the power series partial sum max The allowable error threshold e on both sides of the equation, the final stop error threshold epsilon, find any feasible point as the initial point X 0 ＝X(0)；
S222, giving a power series part and X (S) of a solution function vector X with respect to a variable S;
s223, substituting the power series X (S) into the differential power system to obtain an equation taking the power series expansion coefficient as an unknown number;
specifically, f (X (s)), DH (X (s)) are calculated according to the corresponding rule,
Figure BDA0003168746010000074
s224, comparing the same power series of S in the step S223, calculating each power series coefficient of X (S), and constructing a piecewise rational approximation function according to the power series information;
the elementary operation and elementary function rules about the solution function power series are as follows: taking the unitary power function as an example, other multivariate elementary functions can be modeled to derive rules from the power function. The general form of the unitary power function is:
f(x(s))＝x n (s)
the derivative of s on two sides can be obtained:
x(s)·[f′(x(s))·x′(s)]＝nf(x(s))·x′(s)
the method comprises the following steps:
∑ q≥0 x[q]s q ·∑ q≥0 (q+1)f[q+1]s q ＝n∑ q≥0 f[q]s q ·∑ q≥0 (q+1)x[q+1]s q
here, comparing the two coefficients yields:
Figure BDA0003168746010000075
in this case, fq is obtained in turn, and the power series expansion of f (x (s)) is obtained.
Calculation (DH (X (s)) T ) -1 And (3) recording:
Figure BDA0003168746010000081
/>
Figure BDA0003168746010000082
(11) Wherein the two matrices satisfy:
Figure BDA0003168746010000083
comparing the above two-sided coefficients, the following linear equation set can be obtained:
Figure BDA0003168746010000084
Figure BDA0003168746010000085
Figure BDA0003168746010000086
that is, solving:
M[0]·Γ(:，j)[0]＝I j
here Γ (: j) represents the j-th column of Γ, I j Column vectors [0, …,1, …,0 ] representing the jth number of 1] T 。
A kind of electronic device with high-pressure air-conditioning system:
M[0]·Γ(:,j)[i]＝-U j
here, U j The j' th component of (2) is
Figure BDA0003168746010000087
By solving a linear equation set composed of elements of the matrix of power series coefficients corresponding to Γ(s) times, DH (X (s)) can be calculated T ) -1 。
F (X (s)) calculated, DH (X (s)),
Figure BDA0003168746010000088
(DH(X(s))DH(X(s)) T ) -1 expression, substituting (9) to obtain:
Figure BDA0003168746010000089
comparing the same power coefficient of s to obtain:
Figure BDA0003168746010000091
solving a system of linear equations satisfied by X [ i+1] by the following sequence:
Figure BDA0003168746010000092
all power series coefficients in (10) are solved.
S225, substituting the value of the piecewise rational approximation function at s=s' into the differential power system, i.e.
Figure BDA0003168746010000093
Comparing whether the modulus of the difference between the left side and the right side of the equation is smaller than a preset threshold e to judge whether the power series converges at s';
s226, if the modulus of the difference between the left side and the right side of the equation is smaller than a preset threshold value e, expanding S 'and returning to the step S225, and finding S' which is as large as possible and meets the condition;
s227, if the modulus of the difference between the left side and the right side of the equation is not smaller than a preset threshold e, shrinking S' and returning to the step S225 until the modulus of the difference between the left side and the right side of the equation is smaller than the preset threshold e;
specifically, a rational approximation function is set at s=s 0 The values are substituted into equation (5), and whether the difference value between the left and right sides of the equation is smaller than a preset allowable threshold e is compared. If so, expand s 0 Until it is not satisfied; if not, reduce s 0 Until satisfied. I.e. finding s as large as possible and smaller than the threshold e 0 。
S228, taking X (S') as a new starting point X 0 ；
S229, looping steps S223-S228, calculating a solution function X (S) and a constant S represented by a piecewise rational approximation function * Wherein s is * So that
Figure BDA0003168746010000094
Hold, within the tolerance range +.>
Figure BDA0003168746010000095
Obtaining an approximation of the stable equilibrium point X (s * )；
S2210, approximation of stable equilibrium point X (S * ) The approximate value of the local optimal solution of the optimal power flow problem is obtained.
Specifically, a rational approximation function X (s * ) Sum s * After that, X(s) * ) Is the stable equilibrium point required by us, has theoryIt has been demonstrated that: the stable equilibrium point corresponds to the locally optimal solution of the original optimization problem (2), namely:
Figure BDA0003168746010000096
wherein z is * Is corresponding to the optimal solution x * Is a relaxation variable of (a).
Further as a preferred embodiment of the method, the step of comparing the obtained approximation values of the plurality of locally optimal solutions based on the global search to obtain an approximately globally optimal solution specifically includes:
s31, circulating the step S22 until the preset times are reached, and obtaining a plurality of local optimal solutions;
s32, comparing the plurality of local optimal solutions, and selecting the smallest local optimal solution as an approximate global optimal solution.
Specifically, the global search method is applied, step S22 is repeated, and by comparing a plurality of local optimal solutions, the smallest one is selected as the near global optimal solution, that is, the near global optimal solution corresponding to the optimal power flow problem, which includes:
Figure BDA0003168746010000101
thereby obtaining an optimal power flow scheduling scheme: comprising n b * 1-dimensional optimum bus voltage amplitude
Figure BDA0003168746010000102
And angle->
Figure BDA0003168746010000103
n g * Active power of 1-dimensional optimal generator>
Figure BDA0003168746010000104
And reactive power->
Figure BDA0003168746010000105
Substituting them into the objective function/>
Figure BDA0003168746010000106
The optimum value of the objective function can be obtained +.>
Figure BDA0003168746010000107
Through the steps, the optimal power flow problem under the constraint conditions of meeting the line structure, the maximum current or power flow transmitted by the line, the allowable voltage range of the bus and the like is solved. By the method, the optimal power generation node configuration scheme with the economic benefit and the social benefit as objective functions can be calculated, and then the optimal scheduling strategy is provided for the power system scheduling center, so that the power system reduces the power generation cost as much as possible on the premise of safety and reliability, and improves the economic benefit and the social benefit.
The method of the invention can effectively overcome the calculation difficulty in the traditional method, and specifically: in the process of converting the optimal power flow problem into the initial value problem for solving the ordinary differential equation, the method comprises the task of inverting the function matrix. It should be noted that inverting the function matrix is often difficult to achieve using conventional approaches. The power series of each element in the inverse matrix of the function matrix can be calculated rapidly and efficiently by the FFHE method, namely, the functions of each element in the original matrix and the matrix to be solved are expanded into the power series, the power series of each element in the inverse matrix of the function matrix can be calculated by multiplying the two matrices to be equal to the property of the identity matrix and comparing the coefficients of the same class of terms on the left and right sides of the equation.
The method has high calculation efficiency and high convergence speed, and is particularly characterized in that: aiming at the problems of slow convergence and the like in the process of solving the optimal power flow problem and an equivalent power system in the traditional iterative optimization method and the traditional calculation method of a normal differential equation, the high-precision approximation strategy of the FFHE method can be utilized for large-stride piecewise approximation, and the approximation value of the stable balance point of the corresponding power system can be obtained by calculating a small number of intermediate transition points, which corresponds to the approximation value of the local optimal solution of the optimal power flow problem.
The method saves a large amount of storage space in the calculation process, and specifically: in the process of solving the constructed equivalent power system, the methods such as the Dragon-Kutta method based on the traditional iterative thought need to store a large number of function values of intermediate points to approximate the describing solution curve. In contrast, the method only needs to calculate a small amount of intermediate transition points and store information such as the coefficients of the piecewise rational approximation function of each solution function on the variable and the effective interval length, and can save a large amount of storage space.
The method can efficiently obtain high-precision numerical solutions, and specifically: the solution method based on FFHE uses a piecewise rational approximation method to construct a solution function, and has higher accuracy advantage in numerical calculation compared with the traditional method. In addition, in the numerical simulation, the segmented rational approximation function can be selected as the segmented Pade approximation function, and the value of the Pade approximation function at a certain position can be obtained only by calculating two determinant, so that the method has the advantage of higher calculation efficiency compared with the method for sequentially solving the coefficients of the Pade approximation function.
The method of the invention can use classical mathematical theory to determine the upper error limit of the solution, in particular: the solution method based on FFHE can obtain an analytical expression of the approximate solution, the difference between the left side and the right side of the equation can be calculated by calculating the derivative of the approximate solution and substituting the derivative into the original differential power system, and the error upper bound can be strictly determined by utilizing classical mathematical theory.
The optimal power flow has different application functions in different occasions, the following table lists the main application directions of the optimal power flow, and a person skilled in the art can change, modify, replace and deform the objective function, the control variable and the constraint condition according to specific application problems.
TABLE 1 different applications of optimal power flow in electric power systems
Figure BDA0003168746010000111
While the preferred embodiment of the present invention has been described in detail, the invention is not limited to the embodiment, and various equivalent modifications and substitutions can be made by those skilled in the art without departing from the spirit of the invention, and these modifications and substitutions are intended to be included in the scope of the present invention as defined in the appended claims.

Claims (2)

1. The fast and flexible full-pure embedded power system optimal power flow assessment method is characterized by comprising the following steps of:
s1, acquiring power grid data and establishing an optimal power flow calculation model;
s21, converting the optimal power flow problem into an equation constraint optimization problem according to an optimal power flow model, and establishing an equivalent differential power system;
the differential power system can be expressed as follows;
Figure FDA0004191756600000011
in the above formula, X is an optimization variable, s is an embedding variable,
Figure FDA0004191756600000012
refers to orthogonal projection of the gradient of the objective function on the constraint plane tangent space;
s22, solving an approximation value of a stable balance point of the differential power system based on a piecewise rational approximation method to obtain an approximation value of a local optimal solution of the optimal power flow problem;
the step of solving the approximation value of the stable balance point of the differential power system based on the piecewise rational approximation method to obtain the approximation value of the local optimal solution of the optimal power flow problem specifically comprises the following steps:
s221, initializing parameters, and setting the order q of the power series partial sum max The allowable error threshold e on both sides of the equation, the final stop error threshold epsilon, find any feasible point as the initial point X 0 ＝X(0)；
S222, giving a power series X (S) of the solution function vector X with respect to S;
s223, substituting the power series X (S) into the differential power system to obtain an equation taking the power series expansion coefficient as an unknown number;
s224, comparing the same power series of S in the step S223, calculating each power series coefficient of X (S), and constructing a piecewise rational approximation function according to the power series information;
s225, substituting the value of the piecewise rational approximation function at s=s' into the differential power system, i.e.
Figure FDA0004191756600000013
Figure FDA0004191756600000014
Comparing whether the modulus of the difference between the left side and the right side of the equation is smaller than a preset threshold e to judge whether the power series converges at s';
s226, if the modulus of the difference between the left side and the right side of the equation is smaller than a preset threshold value e, expanding S 'and returning to the step S225, and finding S' which is as large as possible and meets the condition;
s227, if the modulus of the difference between the left side and the right side of the equation is not smaller than a preset threshold e, shrinking S' and returning to the step S225 until the modulus of the difference between the left side and the right side of the equation is smaller than the preset threshold e;
s228, taking X (S') as a new starting point X 0 ；
S229, looping steps S223-S228, calculating a solution function X (S) and a constant S represented by a piecewise rational approximation function * Wherein s is * So that
Figure FDA0004191756600000015
Hold, within the tolerance range +.>
Figure FDA0004191756600000016
Obtaining an approximation of the stable equilibrium point X (s * )；
S2210, approximation of stable equilibrium point X (S * ) The approximate value of the local optimal solution of the optimal power flow problem is obtained;
s3, comparing the obtained approximate values of the plurality of local optimal solutions based on global search to obtain an approximate global optimal solution;
and S4, evaluating an optimal power flow scheduling scheme according to the approximate global optimal solution.
2. The method for evaluating the optimal power flow of the rapid and flexible fully-pure embedded power system according to claim 1, wherein the step of comparing the obtained approximation values of the plurality of local optimal solutions based on global search to obtain the approximate global optimal solution specifically comprises the following steps:
s31, circulating the steps S21-S22 until the preset times are reached, and obtaining the approximate values of a plurality of local optimal solutions;
s32, comparing the approximate values of the plurality of local optimal solutions, and selecting the approximate value of the smallest local optimal solution as the approximate global optimal solution.
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