CN113489014A - Rapid and flexible full-pure embedded type power system optimal power flow evaluation method - Google Patents

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

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CN113489014A
CN113489014A CN202110812483.5A CN202110812483A CN113489014A CN 113489014 A CN113489014 A CN 113489014A CN 202110812483 A CN202110812483 A CN 202110812483A CN 113489014 A CN113489014 A CN 113489014A
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power flow
power
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power system
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CN113489014B (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

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Abstract

The invention discloses a quick, flexible and fully-pure embedded type power system optimal power flow evaluation 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 approximate value of a stable balance point to obtain an approximate value of a local optimal solution; comparing the obtained approximate values of the local optimal solutions based on global search to obtain an approximate global optimal solution; and evaluating the optimal power flow scheduling scheme according to the approximate global optimal solution. The invention provides a quick, flexible and fully-pure embedded method combined with a global search technology, which can quickly and efficiently calculate the approximate value of the stable balance point of the corresponding differential power system obtained by conversion according to the optimization problem, obtain the local optimal solution corresponding to the optimal power flow problem, and solve the problem of low convergence speed of the traditional optimization method. The method for evaluating the optimal power flow of the fully-pure embedded power system can be widely applied to the field of the optimal power flow.

Description

Rapid and flexible full-pure embedded type power system optimal power flow evaluation method
Technical Field
The invention relates to the field of optimal power flow, in particular to a quick, flexible and fully-pure embedded type power system optimal power flow evaluation method.
Background
The Optimal Power Flow (OPF) refers to an optimization process for adjusting parameters of various control devices in a system from the perspective of Optimal operation of a Power system and minimizing an objective function under the constraints 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 method is widely applied to the aspects of safe operation, economic dispatching, power grid planning, reliability analysis of a complex power system, economic control of transmission blockage and the like of the power system. Optimal power flow is a typical nonlinear optimization problem, and the scale and constraint complexity of a complex power system make it more 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 quick, flexible and fully-pure embedded power system optimal power flow evaluation method, and the method solves the defects of low convergence speed and irregular convergence domain of the conventional optimization method.
The first technical scheme adopted by the invention is as follows: a quick, flexible and fully-pure embedded type power system optimal power flow evaluation 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 approximate value of a stable balance point to obtain an approximate value of a local optimal solution;
s3, comparing the obtained approximate values of the local optimal solutions based on the global search technology to obtain an approximate global optimal solution;
and S4, evaluating the optimal power flow scheduling scheme according to the approximate global optimal solution.
Further, the step of acquiring the power grid data and establishing the optimal power flow calculation model specifically includes:
s11, acquiring power grid data;
s12, determining a target function according to the power generation cost data of the generator node;
s13, determining a constraint set according to the 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 power grid node data in the power grid data;
s132, determining an inequality constraint set N according to the line constraint data and the line structure data in the power grid data;
and 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 an approximate value of a stable balance point to obtain an approximate value of a local optimal solution specifically includes:
s21, converting the optimal power flow problem into an equality constraint optimization problem according to the optimal power flow model, and establishing an equivalent differential power system;
s22, solving the approximate value of the stable balance point of the differential power system based on the piecewise rational approximation method to obtain the approximate value of the local optimal solution of the optimal power flow problem.
Further, the differential engine 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 constrained planar tangent space.
Further, the step of solving an approximate value of a stable equilibrium point of the differential power system based on the piecewise rational approximation method to obtain an approximate value of a local optimal solution of the optimal power flow problem specifically includes:
s221, initializing parameters, and setting the order q of the power series partial summaxThe allowable error threshold e and the final stop error threshold epsilon on both sides of the equation, and finding any feasible point as the initial point X0＝X(0)；
S222, providing a power series part of a solution function vector X relative to time S and X (S);
s223, substituting the power series part and X (S) into a differential power system to obtain an equation with a power series expansion coefficient as an unknown number;
s224, comparing the power series with the same degree of S in the step S223, calculating various power series coefficients of X (S), and constructing a segmented 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 powertrain, 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 value e to judge whether the power series converges at the position s';
s226, if the modulus meeting 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 to find 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 value e, reducing 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 value e;
s228, using X (S') as new starting point X0；
S229, looping steps S223-S228, calculating a solution function X (S) and a constant S represented by the piecewise rational approximation function*Wherein s is*So that
Figure BDA0003168746010000031
Is established within an allowable error range
Figure BDA0003168746010000032
Obtaining an approximate value X(s) of a stable equilibrium point*)；
S2210, approximation of stable equilibrium point X (S)*) And the local optimal solution of the optimal power flow problem is an approximate value.
Further, the power series part of the solution function vector X with respect to time s and the expression of X(s) are as follows:
Figure BDA0003168746010000033
in the above formula, Xk(s) represents the power series portion and the kth component of the vector X(s), Xk[i]Represents the power series part and the coefficient of the i-th power term of the k-th component of the vector x(s) with respect to the variable s.
Further, the step of comparing the obtained approximate 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 to obtain a plurality of local optimal solutions;
and S32, comparing the local optimal solutions, and selecting the minimum local optimal solution as an approximate global optimal solution.
The method has the beneficial effects that: the optimal power flow problem is converted into an initial value problem for solving an ordinary differential equation, a stable balance point of a corresponding differential power system is calculated quickly and efficiently by combining a quick, flexible and fully pure embedded method of a global search technology, and an approximate global optimal solution corresponding to the optimal power flow problem is found, so that power grid scheduling is optimized.
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FIG. 1 is a schematic diagram of an embodiment of the present invention for providing a dispatching center with an optimal power flow of a power grid;
fig. 2 is an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments. The step numbers in the following embodiments are provided only for convenience of illustration, the order between the steps is not limited at all, and the execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.
The invention is a fast flexible full-pure embedded method (FFHE) combined with the global search technology, fast and efficiently calculates the stable balance point of a differential power system, namely a local optimal solution corresponding to the optimal power flow problem, and solves the defects of low convergence speed and irregular convergence domain of the traditional optimization method; meanwhile, the defects that the inverse of a function matrix cannot be solved in the process of solving a differential power system by using the conventional ordinary differential equation solving method, the calculated amount is large, the consumed time is long, the storage space is large and the like are overcome.
Referring to fig. 1 and 2, the invention provides a fast, flexible and fully-pure embedded power system optimal power flow evaluation 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 approximate value of a stable balance point to obtain an approximate value of a local optimal solution;
s3, comparing the obtained approximate values of the local optimal solutions based on the global search technology to obtain an approximate global optimal solution;
and S4, evaluating the 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 a target function according to the power generation cost data of the generator node;
s13, determining a constraint set according to the 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 composed of nbVoltage amplitude V of 1DmAnd an angle theta, ngActive power P of 1D generatorgAnd reactive power QgAnd (4) forming.
Figure BDA0003168746010000041
The objective function we need to optimize is f (x) a single polynomial or other non-linear cost function of the active and reactive power of each generator
Figure BDA0003168746010000042
And
Figure BDA0003168746010000043
the sum of (1):
Figure BDA0003168746010000044
Figure BDA0003168746010000045
is the active power corresponding to the ith generator
Figure BDA0003168746010000046
And reactive power
Figure BDA0003168746010000047
A single polynomial or other non-linear cost function.
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 power grid node data in the power grid data;
s132, determining an inequality constraint set N according to the line constraint data and the line structure data in the power grid data;
and 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 constraint set of equations E is composed of 2 nbA non-linear active power and a reactive powerThe rate balance equation consists of:
gP(θ,Vm,Pg)＝0
gQ(θ,Vm,Qg)＝0
the inequality constraint set N is composed of two groups, each group NgThe flow limit of each branch, usually voltage magnitude VmAnd a non-linear function of the angle θ, where hfIs the starting limit value, h, of each branchtIs the termination end limit for each branch:
hf(θ，Vm)＝|Ff(θ，Vm)|-Fmax≤0
ht(θ，Vm)＝|Ft(θ，Vm)|-Fmax≤0
wherein the flow rate FfTypically apparent power flow, but also active power flow or current flow, i.e.:
Figure BDA0003168746010000051
in addition, the voltage amplitude V of the bus is relative to the bus reference angle thetamActive power PgAnd reactive power QgThe 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 approximate value of a stable equilibrium point to obtain an approximate value of a local optimal solution specifically includes:
s21, converting the optimal power flow problem into an equality constraint optimization problem according to the optimal power flow model, and establishing an equivalent differential power system;
specifically, the above optimal power flow problem may be described in the form of:
minf(x)
S.t.gi(x)≤0i＝1，……，m
hj(x)＝0j＝1，……，l (1)
wherein
Figure BDA0003168746010000056
Is an objective function, gi(x) Represents the ith inequality constraint, hj(x) Representing the jth equality constraint. We introduce m relaxation variables ziAnd (3) equivalently converting the optimization problem into the following equations respectively corresponding to the m inequality constraints in the formula (1):
minf(x)
S.t.gi(x)+zi 2＝0i＝1，……，m
hj(x)＝0j＝1，……，l (2)
at this time, the optimal power flow problem becomes an optimization problem with l + m equality constraints, and for convenience of the following expression, we express the formula (2) optimization problem as:
minf(X)
t.t.H(X)＝0 (3)
wherein H (X) is a function vector of dimension l + m, defining X: ═ X, z]TLet N be 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 constrained planar tangent space.
S22, solving the approximate value of the stable balance point of the differential power system based on the piecewise rational approximation method to obtain the approximate value of the local optimal solution of the optimal power flow problem.
First, for each component in the solution function vector X, we can expand it as a power series with respect to time s:
Figure BDA0003168746010000067
X(0)＝X[0]＝X0 (6)
where at s-0, the system is at the initial point.
The complex function formed by elementary operations on solution function vectors can also be expanded as a power series with respect to the variable s:
Figure BDA0003168746010000068
Figure BDA0003168746010000069
wherein f [ i ]]，H[i]Is about Xk[i′](ii) a k is 1, … …, n + m; i' is less than or equal to i;
similarly, DH can also be considered to relate to Xk[i′]Function of (c):
Figure BDA0003168746010000071
substituting the power series expansion of the equations (6), (7) and (8) with respect to s into the equation (5):
Figure BDA0003168746010000072
by comparing the coefficients of the terms of the same degree for s on both sides of equation (9), the determination of the unknown X can be madek[i](ii) a k is 1, … …, n + m; i is more than or equal to 1.
After the above steps are completed, X can be obtainedk(s); k is 1, …, a power series expression of n + m. And constructing a segmented rational approximation function according to the existing power series information so as to expand the effective interval. And substituting the value of the piecewise rational approximation function at s-s' into the equation (5), and comparing whether the modulus of the difference between the left side and the right side of the equation is larger than a preset allowable threshold value. Finding s' as large as possible makes the modulus of the difference between the left and right sides of the equation smaller than the threshold. Taking X (s') as a new starting point, repeating the steps until s is found*So that
Figure BDA0003168746010000073
Less than the error limit given in advance, so we believe that an approximation of the stable equilibrium point is found.
Further, as a preferred embodiment of the method, the step of solving an approximate value of a stable equilibrium point of the differential power system based on the piecewise rational approximation method to obtain an approximate value of a local optimal solution of the optimal power flow problem specifically includes:
s221, initializing parameters, and setting the order q of the power series partial summaxEtc. ofThe allowable error threshold e and the final stop error threshold epsilon on both sides of the formula are used for finding any feasible point as an initial point X0＝X(0)；
S222, providing a power series part of a solution function vector X relative to a variable S and X (S);
s223, substituting the power series X (S) into a differential power system to obtain an equation with a power series expansion coefficient as an unknown number;
specifically, f (X (s)), DH (X (s)),
Figure BDA0003168746010000074
s224, comparing the power series with the same degree of S in the step S223, calculating various power series coefficients of X (S), and constructing a segmented rational approximation function according to the power series information;
the elementary operation and elementary function rule of the solution function power series are as follows: taking a unitary power function as an example, other multiple elementary functions may be derived from the power function in an analogous manner. The general form of a unitary power function is:
f(x(s))＝xn(s)
the derivation of s on both sides can be obtained:
x(s)·[f′(x(s))·x′(s)]＝nf(x(s))·x′(s)
this time is:
∑q≥0x[q]sq·∑q≥0(q+1)f[q+1]sq＝n∑q≥0f[q]sq·∑q≥0(q+1)x[q+1]sq
the comparison of the two-sided coefficients here yields:
Figure BDA0003168746010000075
in this case, fq is sequentially obtained, and the power series expansion of f (x (s)) is obtained.
Calculation (DH (X (s)))T)-1Recording:
Figure BDA0003168746010000081
Figure BDA0003168746010000082
(11) two matrices satisfy:
Figure BDA0003168746010000083
comparing the coefficients of the two sides of the above equation, the following system of linear equations can be obtained:
Figure BDA0003168746010000084
Figure BDA0003168746010000085
Figure BDA0003168746010000086
that is, solving for:
M[0]·Γ(:，j)[0]＝Ij
here, Γ (: j) denotes the jth column of Γ, IjRepresents the j-th 1 column vector [0, 0, …, 1, …,0]T。
And:
M[0]·Γ(:,j)[i]＝-Uj
here, UjThe jth component of (a) is
Figure BDA0003168746010000087
By solving a linear equation set composed of the elements of the matrix of power series coefficients corresponding to each order of Γ(s), it is possible to calculate (DH (X (s)))T)-1。
F (X (s)) and DH (X) obtained by calculation(s)),
Figure BDA0003168746010000088
(DH(X(s))DH(X(s))T)-1And (3) substituting the expression into the formula (9) to obtain:
Figure BDA0003168746010000089
comparing the coefficients of the powers of the orders s yields:
Figure BDA0003168746010000091
solving a system of linear equations satisfied by X [ i +1], in the following order:
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 powertrain, 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 value e to judge whether the power series converges at the position s';
s226, if the modulus meeting 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 to find 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 value e, reducing 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 value e;
in particular, the rational approximation function is defined as s ═ s0Substituting the value into an equation (5), and comparing whether the difference value between the left side and the right side of the equation is smaller than a preset allowable threshold value e. If so, then s is expanded0Until not satisfied; if not, then reduces0Until satisfied. I.e. finding s as large as possible and smaller than the threshold e0。
S228, using X (S') as new starting point X0；
S229, looping steps S223-S228, calculating a solution function X (S) and a constant S represented by the piecewise rational approximation function*Wherein s is*So that
Figure BDA0003168746010000094
Is established within an allowable error range
Figure BDA0003168746010000095
Obtaining an approximate value X(s) of a stable equilibrium point*)；
S2210, approximation of stable equilibrium point X (S)*) And the local optimal solution of the optimal power flow problem is an approximate value.
Specifically, a rational approximation function X(s) satisfying a termination condition is found*) And s*Then, X(s)*) Is the point of stable equilibrium we require, it has been theoretically 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*The relaxation variable of (2).
Further, as a preferred embodiment of the method, the step of comparing the obtained approximate values of the plurality of local optimal solutions based on the global search to obtain an approximate global optimal solution specifically includes:
s31, circulating the step S22 until the preset times are reached to obtain a plurality of local optimal solutions;
and S32, comparing the local optimal solutions, and selecting the minimum local optimal solution as an approximate global optimal solution.
Specifically, by using a global search method, repeating step S22, and comparing a plurality of local optimal solutions, selecting the smallest solution as an approximate global optimal solution, that is, an approximate global optimal solution corresponding to the optimal power flow problem, the following steps are performed:
Figure BDA0003168746010000101
thereby obtaining an optimal power flow scheduling scheme: containing nb1-dimensional optimal bus voltage amplitude
Figure BDA0003168746010000102
And angle
Figure BDA0003168746010000103
ng1-dimensional optimal active power of generator
Figure BDA0003168746010000104
And reactive power
Figure BDA0003168746010000105
Substitute them into the objective function
Figure BDA0003168746010000106
The optimal 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 constraint conditions of a 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 applying the method, the optimal power generation node configuration scheme with economic benefit and social benefit as target functions can be calculated, and then the optimal scheduling strategy is provided for the power system scheduling center, so that the power generation cost of the power system is reduced as much as possible on the premise of safety and reliability, and the economic benefit and the social benefit are improved.
The method of the invention can effectively overcome the calculation difficulty in the traditional method, in particular to the following steps: in the process of converting the optimal power flow problem into an initial value problem for solving an ordinary differential equation, the task of function matrix inversion is included. It should be noted that inverting the function matrix in the conventional manner is often difficult to achieve. The power series of each element in the inverse matrix of the function matrix can be rapidly and efficiently calculated through an FFHE method, namely, the functions on each element in the original matrix and the inverse matrix to be solved are expanded into the power series, and the power series of each element in the inverse matrix of the function matrix can be calculated by utilizing the property that the multiplication of the two matrixes is equal to that of a unit matrix and comparing the left coefficient and the right coefficient of the same kind of terms of an equation.
The method of the invention has high calculation efficiency and high convergence speed, and particularly comprises the following steps: 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 the ordinary differential equation, the high-precision approximation strategy of the FFHE method can be used for carrying out large-stride piecewise approximation, and the approximation of the stable balance point of the corresponding power system and the approximation of the local optimal solution corresponding to the optimal power flow problem can be obtained by calculating a small number of intermediate transition points.
The method saves a large amount of storage space in the calculation process, and particularly comprises the following steps: in the process of solving the constructed equivalent power system, the method of the Runge-Kutta and the like based on the traditional iteration thought needs to store a large number of function values of intermediate points to approximately describe a solution curve. Compared with the prior art, the method only needs to calculate a small number of intermediate transition points and store the information of each solution function about each coefficient of the piecewise rational approximation function of the variable, the effective interval length and the like, and can save a large amount of storage space.
The method can efficiently obtain a high-precision numerical solution, and specifically comprises the following steps: the FFHE-based solution method uses a piecewise rational approximation method to construct a solution function, and has the advantage of higher precision in numerical calculation compared with the traditional method. In addition, in numerical simulation, the piecewise rational approximation function can be selected as the piecewise Pade approximation function, and the value of the Pade approximation function at a certain position can be obtained only by calculating two determinants.
The method of the invention can use the classical mathematical theory to determine the upper limit of the error of the solution, specifically: an analytic expression of an approximate solution can be obtained by a solution method based on the FFHE, the difference between the left side and the right side of an equation can be calculated by calculating the derivative of the approximate solution and substituting the derivative into an original differential power system, and the upper error bound can be strictly determined by using a classical mathematical theory.
The optimal power flow has different application functions in different occasions, the following table lists a plurality of 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 in the patent according to specific application problems.
Table 1 different applications of optimal power flow in power systems
Figure BDA0003168746010000111
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. A quick, flexible and fully-pure embedded type power system optimal power flow evaluation method is characterized by comprising 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 approximate value of a stable balance point to obtain an approximate value of a local optimal solution;
s3, comparing the obtained approximate values of the local optimal solutions based on global search to obtain an approximate global optimal solution;
and S4, evaluating the optimal power flow scheduling scheme according to the approximate global optimal solution.
2. The method for rapid, flexible and fully-embedded optimal power flow evaluation of a power system according to claim 1, wherein the step of establishing a differential power system based on an optimal power flow calculation model and solving an approximation of a stable equilibrium point to obtain an approximation of a local optimal solution specifically comprises:
s21, converting the optimal power flow problem into an equality constraint optimization problem according to the optimal power flow model, and establishing an equivalent differential power system;
s22, solving the approximate value of the stable balance point of the differential power system based on the piecewise rational approximation method to obtain the approximate value of the local optimal solution of the optimal power flow problem.
3. The method for rapid, flexible and fully-embedded power system optimal power flow assessment according to claim 2, wherein the differential power system is expressed as follows:
Figure FDA0003168745000000011
in the above formula, X is an optimization variable, s is an embedding variable, t is a time variable of the power system,
Figure FDA0003168745000000012
refers to the orthogonal projection of the gradient of the objective function onto the constrained planar tangent space.
4. The method for rapidly, flexibly and fully-embedded optimal power flow evaluation of an electric power system according to claim 3, wherein the step of solving the approximate value of the stable equilibrium point of the differential power system based on the piecewise rational approximation method to obtain the approximate value of the local optimal solution of the optimal power flow problem specifically comprises:
s221, initializing parameters, and setting the order q of the power series partial summaxThe allowable error threshold e and the final stop error threshold epsilon on both sides of the equation, and finding any feasible point as the initial point X0＝X(0)；
S222, providing a power series X (S) of a solution function vector X relative to time S;
s223, substituting the power series X (S) into a differential power system to obtain an equation with a power series expansion coefficient as an unknown number;
s224, comparing the power series with the same degree of S in the step S223, calculating various power series coefficients of X (S), and constructing a segmented 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 powertrain, i.e.
Figure FDA0003168745000000013
Figure FDA0003168745000000021
Comparing whether the modulus of the difference between the left side and the right side of the equation is smaller than a preset threshold value e to judge whether the power series converges at the position s';
s226, if the modulus meeting 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 to find 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 value e, reducing 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 value e;
s228, using X (S') as new starting point X0；
S229, looping steps S223-S228, calculating a solution function X (S) and a constant S represented by the piecewise rational approximation function*Wherein s is*So that
Figure FDA0003168745000000022
Is established within an allowable error range
Figure FDA0003168745000000023
Obtaining an approximate value X(s) of a stable equilibrium point*)；
S2210, approximation of stable equilibrium point X (S)*) And the local optimal solution of the optimal power flow problem is an approximate value.
5. The method for rapidly, flexibly and fully-embedded optimal power flow evaluation of a power system according to claim 4, wherein the step of comparing the obtained approximate values of the plurality of local optimal solutions based on global search to obtain an approximate global optimal solution specifically comprises:
s31, circulating the step S2 until reaching the preset times to obtain approximate values of a plurality of local optimal solutions;
and S32, comparing the approximate values of the local optimal solutions, and selecting the approximate value of the minimum local optimal solution as the approximate global optimal solution.
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