WO2023000807A1 - 一种快速灵活全纯嵌入式电力***最优潮流评估方法 - Google Patents

一种快速灵活全纯嵌入式电力***最优潮流评估方法 Download PDF

Info

Publication number
WO2023000807A1
WO2023000807A1 PCT/CN2022/094899 CN2022094899W WO2023000807A1 WO 2023000807 A1 WO2023000807 A1 WO 2023000807A1 CN 2022094899 W CN2022094899 W CN 2022094899W WO 2023000807 A1 WO2023000807 A1 WO 2023000807A1
Authority
WO
WIPO (PCT)
Prior art keywords
optimal
power flow
approximate
power
solution
Prior art date
Application number
PCT/CN2022/094899
Other languages
English (en)
French (fr)
Inventor
汪涛
谭伟鹏
张文
刘彦志
张佳敏
Original Assignee
中山大学
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 中山大学 filed Critical 中山大学
Publication of WO2023000807A1 publication Critical patent/WO2023000807A1/zh

Links

Images

Classifications

    • 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

Definitions

  • the invention relates to the field of optimal power flow, in particular to a fast, flexible and purely embedded power system optimal power flow evaluation method.
  • Optimal Power Flow refers to adjusting the parameters of various control devices in the system from the perspective of optimal operation of the power system, and realizing the minimization of the objective function under the constraints of the normal power balance of nodes and various safety indicators. the optimization process. Since optimal power flow is an analysis method that considers the security and economy of the network at the same time, it has been widely used in the safe operation of power systems, economic dispatch, power grid planning, reliability analysis of complex power systems, and economic control of transmission congestion. application.
  • Optimal power flow is a typical nonlinear optimization problem.
  • the scale of complex power systems and the complexity of constraints make it difficult to solve this nonlinear optimization problem robustly and efficiently.
  • the purpose of the present invention is to provide a fast and flexible optimal power flow evaluation method for a purely embedded power system, which solves the problems of slow convergence speed and irregular convergence domain of existing traditional optimization methods.
  • the first technical solution adopted by the present invention is: a method for evaluating the optimal power flow of a fast, flexible and pure embedded power system, comprising the following steps:
  • step of acquiring power grid data and establishing an optimal power flow calculation model specifically includes:
  • step of determining the constraint set according to the grid data specifically includes:
  • the step of establishing a differential dynamic system based on the optimal power flow calculation model and solving the approximate value of the stable equilibrium point to obtain the approximate value of the local optimal solution specifically includes:
  • differential dynamical system can be expressed as follows:
  • X is the optimization variable
  • s is the embedded variable
  • t is the time variable of the dynamical system
  • the step of solving the approximate value of the stable equilibrium point of the differential dynamic system based on the piecewise rational approximation method, and obtaining the approximate value of the local optimal solution of the optimal power flow problem specifically includes:
  • step S224 comparing the same power series about s in step S223, and calculating the power series coefficients of X(s), constructing a piecewise rational approximation function according to the power series information;
  • step S227 If it is not satisfied that the modulus of the difference between the left and right sides of the equation is smaller than the preset threshold e, reduce s' and return to step S225 until the modulus of the difference between the left and right sides of the equation is smaller than the preset threshold e;
  • the approximate value X(s * ) of the stable equilibrium point is the approximate value of the local optimal solution of the optimal power flow problem.
  • X k (s) represents the power series part and the kth component of the vector X(s)
  • X k [i] represents the power series part and the kth component of the vector X(s) with respect to the variable s
  • the i-th power term coefficient
  • the step of obtaining an approximate global optimal solution by comparing the approximate values of multiple local optimal solutions obtained based on the global search technology specifically includes:
  • step S31 Repeat step S2 until the preset number of times is reached to obtain multiple local optimal solutions;
  • the beneficial effect of the method of the present invention is: the present invention transforms the optimal power flow problem into the initial value problem for solving the ordinary differential equation, and calculates the corresponding differential dynamic system quickly and efficiently through the fast and flexible holomorphic embedded method combined with the global search technology
  • the stable equilibrium point of the system can find the approximate global optimal solution corresponding to the optimal power flow problem, so as to optimize the power grid dispatching.
  • Fig. 1 is the schematic diagram that the specific application embodiment of the present invention provides the optimal power flow of power grid for dispatching center;
  • Fig. 2 is a specific embodiment of the present invention.
  • the present invention is a fast and flexible holomorphic embedded method (FFHE) combined with global search technology, which can quickly and efficiently calculate the stable equilibrium point of the differential dynamic system, that is, the local optimal solution corresponding to the optimal power flow problem, and solve the existing traditional optimization method
  • the method has the shortcomings of slow convergence speed and irregular convergence domain; at the same time, it also solves the shortcomings of the existing ordinary differential equation solution method that cannot solve the inverse of the function matrix in the process of solving the differential dynamic system, and has a large amount of calculation, time-consuming, and large storage space.
  • the present invention provides a kind of method for evaluating the optimal power flow of fast and flexible pure embedded power system, and this method comprises the following steps:
  • the step of acquiring power grid data and establishing an optimal power flow calculation model specifically includes:
  • the optimization vector x of the optimal power flow problem generally consists of n b * 1-dimensional voltage amplitude V m and angle ⁇ , and n g * 1-dimensional generator active power P g and reactive power Q g .
  • the objective function we need to optimize is f(x) by a single polynomial or other nonlinear cost function of the active and reactive power of each generator and and of:
  • the step of determining the constraint set according to the grid data specifically includes:
  • Inequality constraint set N consists of two groups, each group n g branch flow limits, usually a nonlinear function of voltage amplitude V m and angle ⁇ , where h f is the initial end limit of each branch, h t is the termination limit value of each branch:
  • the flow rate F f is usually an apparent power flow, but it can also be an active power flow or a current, namely:
  • the step of establishing a differential dynamic system based on the optimal power flow calculation model and solving the approximate value of the stable equilibrium point to obtain the approximate value of the local optimal solution specifically includes:
  • H(X) is a function vector of l+m dimension
  • f(X) as
  • X is the optimization variable
  • s is the embedded variable
  • t is the time variable of the dynamical system
  • the composite function formed by the elementary operation of the solution function vector can also be expanded into a power series with respect to the variable s:
  • DH can also be regarded as a function of X k [i']:
  • the step of solving the approximate value of the stable equilibrium point of the differential dynamic system based on the piecewise rational approximation method and obtaining the approximate value of the local optimal solution of the optimal power flow problem specifically includes:
  • step S224 comparing the same power series about s in step S223, and calculating the power series coefficients of X(s), constructing a piecewise rational approximation function according to the power series information;
  • f[q] can be obtained in turn, and the power series expansion of f(x(s)) can also be obtained.
  • ⁇ (:,j) represents the jth column of ⁇
  • I j represents the column vector [0,0,...,1,...,0,0] T whose jth number is 1.
  • DH(X(s))DH(X(s)) T ) -1 can be calculated by solving the linear equations composed of the elements of the power series coefficient matrix corresponding to each degree of ⁇ (s).
  • step S227 If it is not satisfied that the modulus of the difference between the left and right sides of the equation is smaller than the preset threshold e, reduce s' and return to step S225 until the modulus of the difference between the left and right sides of the equation is smaller than the preset threshold e;
  • the approximate value X(s * ) of the stable equilibrium point is the approximate value of the local optimal solution of the optimal power flow problem.
  • X(s * ) is the stable equilibrium point we require. It has been proved by theory that the stable equilibrium point corresponds to the original optimization problem (2 ) local optimal solution, namely:
  • the step of obtaining an approximate global optimal solution by comparing the approximate values of multiple local optimal solutions obtained based on the global search specifically includes:
  • step S31 Repeat step S22 until the preset number of times is reached, and multiple local optimal solutions are obtained;
  • the global search method is used to repeat step S22, and by comparing multiple local optimal solutions, the smallest one is selected as the approximate global optimal solution, that is, the approximate global optimal solution corresponding to the optimal power flow problem, as follows:
  • the optimal power flow dispatching scheme is obtained: the optimal bus voltage amplitude including n b *1 dimensions and angle dimensional optimal generator active power and reactive power Substitute them into the objective function
  • the optimal value of the objective function can be obtained
  • the method of the invention can effectively overcome the calculation difficulties in the traditional method, specifically: in the process of converting the optimal power flow problem into the initial value problem for solving ordinary differential equations, the task of inverting the function matrix is included. It should be noted that it is usually difficult to find the inverse of a function matrix using traditional methods. We can quickly and efficiently calculate the power series of each element in the inverse matrix of the function matrix through the FFHE method, that is, expand the function on each element in the original matrix and the matrix to be inversed into a power series, and multiply the above two matrices It is equal to the property of the unit matrix, and the power series of each element in the inverse matrix of the function matrix can be calculated by comparing the coefficients of the same items on the left and right sides of the equation.
  • the method of the present invention has high calculation efficiency and fast convergence speed.
  • the slow convergence is shown in the process of solving the above-mentioned optimal power flow problem and the equivalent dynamical system and other problems, we can use the high-precision approximation strategy of the FFHE method to perform segmental approximation in large steps, and calculate a small number of intermediate transition points to obtain the approximate value of the stable equilibrium point of the corresponding dynamical system, which corresponds to the local optimum of the optimal power flow problem. An approximation of the optimal solution.
  • the method of the present invention saves a large amount of storage space in the calculation process, specifically: in the process of solving the constructed equivalent dynamical system, methods such as Runge-Kutta based on traditional iterative ideas need to store a large number of function values of intermediate points to approximate Characterize the solution curve. In contrast, this method only needs to calculate a small number of intermediate transition points and store information such as the coefficients of the piecewise rational approximation function of each variable and the effective interval length of each solution function, which can save a lot of storage space.
  • the method of the invention can efficiently obtain high-precision numerical solutions.
  • the FFHE-based solution method uses a piecewise rational approximation method to construct a solution function, which has higher precision advantages in numerical calculations than traditional methods.
  • the piecewise rational approximation function can be selected as the piecewise Padé approximation function, and only two determinants need to be calculated to obtain the value of the Padé approximation function at a certain place.
  • the coefficients of the German approximation function have the advantage of higher calculation efficiency.
  • the method of the present invention can use classical mathematical theory to determine the upper limit of the error of the solution, specifically: the solution method based on FFHE can obtain the analytical expression of the approximate solution, and by calculating the derivative of the approximate solution, the equation can be calculated in the original differential dynamic system For the difference between the left and right sides, the upper bound of the error can be strictly determined using classical mathematical theory.
  • Optimal power flow has different application functions in different occasions.
  • the following table lists several main application directions of optimal power flow. Those skilled in the art can change the objective function, control variables, and constraints in this patent according to specific application problems, Modify, replace, deform.

Landscapes

  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Supply And Distribution Of Alternating Current (AREA)

Abstract

提供了一种快速灵活全纯嵌入式电力***最优潮流评估方法，包括：获取电网数据并建立最优潮流计算模型；基于最优潮流计算模型建立微分动力***并求解稳定平衡点的近似值，得到局部最优解的近似值；基于全局搜索对获得的多个局部最优解的近似值进行比较，得到近似全局最优解；根据近似全局最优解评估最优潮流调度方案。结合全局搜索技术的快速灵活全纯嵌入式方法，快速高效的计算出根据优化问题转换得到的相应微分动力***的稳定平衡点的近似值，得到对应最优潮流问题的局部最优解，解决现有传统优化方法方法收敛速度慢的问题，可广泛应用于最优潮流领域。

Description

一种快速灵活全纯嵌入式电力***最优潮流评估方法 技术领域
本发明涉及最优潮流领域，尤其涉及一种快速灵活全纯嵌入式电力***最优潮流评估方法。
背景技术
最优潮流(Optimal Power Flow，OPF)是指从电力***优化运行的角度来调整***中各种控制设备的参数，在满足节点正常功率平衡及各种安全指标的约束下，实现目标函数最小化的优化过程。由于最优潮流是同时考虑网络的安全性和经济性的分析方法，因此在电力***的安全运行、经济调度、电网规划、复杂电力***的可靠性分析、传输阻塞的经济控制等方面得到广泛的应用。
技术问题
最优潮流是一个典型的非线性优化问题，复杂电力***的规模和约束的复杂性使得稳健高效地求解此非线性优化问题难度较大。
技术解决方案
为了解决上述技术问题，本发明的目的是提供一种快速灵活全纯嵌入式电力***最优潮流评估方法，解决现有传统优化方法方法收敛速度慢，收敛域不规则的不足。
本发明所采用的第一技术方案是：一种快速灵活全纯嵌入式电力***最优潮流评估方法，包括以下步骤：
S1、获取电网数据并建立最优潮流计算模型；
S2、基于最优潮流计算模型建立微分动力***并求解稳定平衡点的近似值，得到局部最优解的近似值；
S3、基于全局搜索技术对获得的多个局部最优解的近似值进行比较，得到近似全局最优解；
S4、根据近似全局最优解评估最优潮流调度方案。
进一步，所述获取电网数据并建立最优潮流计算模型这一步骤，其具体包括：
S11、获取电网数据；
S12、根据发电机节点的发电成本数据确定目标函数；
S13、根据电网数据确定约束集；
S14、根据目标函数和约束集建立最优潮流计算模型。
进一步，所述根据电网数据确定约束集这一步骤，其具体包括：
S131、根据电网数据中的电网节点数据确定等式约束集E；
S132、根据电网数据中的线路约束数据和线路结构数据确定不等式约束集N；
S133、根据电网数据中的节点功率约束数据、母线电压约束数据和母线参考角度数据确定框约束集B。
进一步，所述基于最优潮流计算模型建立微分动力***并求解稳定平衡点的近似值，得到局部最优解的近似值这一步骤，其具体包括：
S21、根据最优潮流模型将最优潮流问题转化为等式约束的优化问题，建立等价的微分动力***；
S22、基于分段有理逼近方法求解微分动力***稳定平衡点的近似值，得到最优潮流问题的局部最优解的近似值。
进一步，所述微分动力***可表达如下：
Figure PCTCN2022094899-appb-000001
上式中，X为优化变量，s为嵌入变量，t为该动力***的时间变量，
Figure PCTCN2022094899-appb-000002
指目标函数的梯度在约束平面切空间上的正交投影。
进一步，所述基于分段有理逼近方法求解微分动力***稳定平衡点的近似值，得到最优潮流问题的局部最优解的近似值这一步骤，其具体包括：
S221、初始化参数，设定幂级数部分和的阶数q max，等式两边容许误差阈值e，最终停止误差阈值ε，找到任一可行点作为初始点X 0＝X(0)；
S222、给出解函数向量X关于时间s的幂级数部分和X(s)；
S223、将幂级数部分和X(s)代入微分动力***，得到以幂级数展开式系数为未知数的方程；
S224、比较步骤S223中关于s的同次幂级数，并计算出X(s)的各项幂级数系数，根据幂级数信息构造分段有理逼近函数；
S225、将分段有理逼近函数在s＝s'处的值代入微分动力***，即
Figure PCTCN2022094899-appb-000003
比较方程左右两边之差的模是否小于预设阈值e来判断幂级数是否在s'处收敛；
S226、若满足方程左右两边之差的模小于预设阈值e，扩大s'并返回步骤S225，找到尽可能大的且符合条件的s'；
S227、若不满足方程左右两边之差的模小于预设阈值e，缩小s'并返回步骤S225，直至方程左右两边之差的模小于预设阈值e；
S228、将X(s')作为新的起点X 0；
S229、循环步骤S223-S228，计算出由分段有理逼近函数表示的解函数X(s)和常数s *，其中s *使得
Figure PCTCN2022094899-appb-000004
成立，在允许误差范围内
Figure PCTCN2022094899-appb-000005
得到稳定平衡点的近似值X(s *)；
S2210、稳定平衡点的近似值X(s *)，就是最优潮流问题的局部最优解的近似值。
进一步，所述解函数向量X关于时间s的幂级数部分和X(s)的表达式如下：
Figure PCTCN2022094899-appb-000006
上式中，X k(s)代表幂级数部分和向量X(s)的第k个分量，X k[i]代表幂级数部分和向量X(s)第k个分量关于变量s的i次方项系数。
进一步，所述基于全局搜索技术对获得的多个局部最优解的近似值进行比较，得到近似全局最优解这一步骤，其具体包括：
S31、循环步骤S2直至达到预设次数，得到多个局部最优解；
S32、比较多个局部最优解，选取最小的局部最优解作为近似全局最优解。
有益效果
本发明方法的有益效果是：本发明将最优潮流问题转化为求解常微分方程的初值问题，通过结合全局搜索技术的快速灵活全纯嵌入式方法，快速高效的计算出相应的微分动力***的稳定平衡点，找到对应最优潮流问题的近似全局最优解，从而优化电网调度。
附图说明
图1是本发明具体应用实施例为调度中心提供电网最优潮流的示意图；
图2是本发明具体实施例。
本发明的实施方式
下面结合附图和具体实施例对本发明做进一步的详细说明。对于以下实施例中的步骤编号，其仅为了便于阐述说明而设置，对步骤之间的顺序不做任何限定，实施例中的各步骤的执行顺序均可根据本领域技术人员的理解来进行适应性调整。
本发明是结合全局搜索技术的快速灵活全纯嵌入式方法(FFHE)，快速高效的计算出微分动力***的稳定平衡点，即对应最优潮流问题的局部最优解，解决现有传统优化方法方法收敛速度慢，收敛域不规则的不足；同时也解决了现有常微分方程求解方法求解微分动力***过程中无法求解函数矩阵的逆，计算量大，耗时长，存储空间大等的不足。
参照图1和图2，本发明提供了一种快速灵活全纯嵌入式电力***最优潮流评估方法，该方法包括以下步骤：
S1、获取电网数据并建立最优潮流计算模型；
S2、基于最优潮流计算模型建立微分动力***并求解稳定平衡点的近似值，得到局部最优解的近似值；
S3、基于全局搜索技术对获得的多个局部最优解的近似值进行比较，得到近似全局最优解；
S4、根据近似全局最优解评估最优潮流调度方案。
进一步作为本方法的优选实施例，所述获取电网数据并建立最优潮流计算模型这一步骤，其具体包括：
S11、获取电网数据；
S12、根据发电机节点的发电成本数据确定目标函数；
S13、根据电网数据确定约束集；
S14、根据目标函数和约束集建立最优潮流计算模型。
具体地，最优潮流问题的优化向量x一般由n b*1维的电压幅值V m和角度θ，n g*1维发电机有功功率P g和无功功率Q g组成。
Figure PCTCN2022094899-appb-000007
而我们需要优化的目标函数则是f(x)由每个发电机的有功功率和无功功率的单个多项式或其他非线性成本函数
Figure PCTCN2022094899-appb-000008
和
Figure PCTCN2022094899-appb-000009
的和：
Figure PCTCN2022094899-appb-000010
Figure PCTCN2022094899-appb-000011
是对应于第i个发电机的有功功率
Figure PCTCN2022094899-appb-000012
和无功功率
Figure PCTCN2022094899-appb-000013
的单个多项式或其他非线性成本函数。
进一步作为本方法的优选实施例，所述根据电网数据确定约束集这一步骤，其具体包括：
S131、根据电网数据中的电网节点数据确定等式约束集E；
S132、根据电网数据中的线路约束数据和线路结构数据确定不等式约束集N；
S133、根据电网数据中的节点功率约束数据、母线电压约束数据和母线参考角度数据确 定框约束集B。
具体地，等式约束集E是由2*n b个非线性有功功率和无功功率平衡方程组成：
g P(θ,V m,P g)＝0
g Q(θ,V m,Q g)＝0
不等式约束集N由两组，每组n g个支路流量限值组成，通常是电压幅值V m和角度θ的非线性函数，其中h f是每条支路的起始端限值，h t是每条支路的终止端限值：
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
其中流量F f通常是视在功率流，但也可以是有功功率流或者是电流，即：
Figure PCTCN2022094899-appb-000014
此外，还有对母线参考角度θ，母线的电压幅值V m，有功功率P g和无功功率Q g的框约束集B：
Figure PCTCN2022094899-appb-000015
Figure PCTCN2022094899-appb-000016
Figure PCTCN2022094899-appb-000017
Figure PCTCN2022094899-appb-000018
进一步作为本方法优选实施例，所述基于最优潮流计算模型建立微分动力***并求解稳定平衡点的近似值，得到局部最优解的近似值这一步骤，其具体包括：
S21、根据最优潮流模型将最优潮流问题转化为等式约束的优化问题，建立等价的微分动力***；
具体地，以上最优潮流问题可以描述为以下形式：
min f(x)
S.t.g i(x)≤0i＝1,……,m
h j(x)＝0j＝1,……,l         (1)
其中
Figure PCTCN2022094899-appb-000019
是目标函数，g i(x)代表第i个不等式约束，h j(x)代表第j个等式约束。我们引入m个松弛变量z i，分别对应于(1)式中m个不等式约束，将优化问题等价 转化为：
min f(x)
S.t.g i(x)+z i 2＝0i＝1,……,m
h j(x)＝0j＝1,……,l             (2)
此时最优潮流问题变成了有l+m个等式约束的优化问题，为方便下文表示，我们将(2)式优化问题表示为：
min f(X)
S.t.H(X)＝0            (3)
其中H(X)是l+m维的函数向量,定义X∶＝[x,z] T,令N＝l+m,将f(X)重新定义为
Figure PCTCN2022094899-appb-000020
Figure PCTCN2022094899-appb-000021
Figure PCTCN2022094899-appb-000022
Figure PCTCN2022094899-appb-000023
最后建立等价的微分动力***：
Figure PCTCN2022094899-appb-000024
上式中，X为优化变量，s为嵌入变量，t为该动力***的时间变量，
Figure PCTCN2022094899-appb-000025
指目标函数的梯度在约束平面切空间上的正交投影。
S22、基于分段有理逼近方法求解微分动力***稳定平衡点的近似值，得到最优潮流问题的局部最优解的近似值。
首先，对于解函数向量X中的每一分量，我们都可以将其展开为关于时间s的幂级数：
Figure PCTCN2022094899-appb-000026
X(0)＝X[0]＝X 0          (6)
其中在s＝0处时，***处于初始点处。
由解函数向量初等运算构成的复合函数也可以展开成关于变量s的幂级数：
Figure PCTCN2022094899-appb-000027
Figure PCTCN2022094899-appb-000028
其中f[i],H[i]是关于X k[i']；k＝1,……,n+m；i'≤i的函数；
同样的，DH也可以看成是关于X k[i']的函数：
Figure PCTCN2022094899-appb-000029
将(6)(7)(8)式中关于s的幂级数展开式代入(5)式：
Figure PCTCN2022094899-appb-000030
通过比较(9)式两边关于s的同次项的系数，可以确定关于未知数X k[i]；k＝1,……,n+m；i≥1的方程组。
完成以上步骤后可以得到X k(s)；k＝1,…,n+m的幂级数表达式。根据已有的幂级数信息，构造分段有理逼近函数，以扩大有效区间。将分段有理逼近函数在s＝s'处的值代入方程(5)，比较方程左右两边之差的模是否大于预先设置的可容许的阈值。找到尽可能大的s'，使得方程左右两边之差的模小于该阈值。将X(s')作为新的起点，重复以上步骤，直到找到s *使得
Figure PCTCN2022094899-appb-000031
小于事先给出的误差限，这样我们就认为找到了稳定平衡点的近似值。
进一步作为本方法优选实施例，所述基于分段有理逼近方法求解微分动力***稳定平衡点的近似值，得到最优潮流问题的局部最优解的近似值这一步骤，其具体包括：
S221、初始化参数，设定幂级数部分和的阶数q max，等式两边容许误差阈值e，最终停止误差阈值ε，找到任一可行点作为初始点X0＝X(0)；
S222、给出解函数向量X关于变量s的幂级数部分和X(s)；
S223、将幂级数X(s)代入微分动力***，得到以幂级数展开式系数为未知数的方程；
具体地，根据相应规则计算f(X(s)),DH(X(s)),
Figure PCTCN2022094899-appb-000032
S224、比较步骤S223中关于s的同次幂级数，并计算出X(s)的各项幂级数系数，根据幂级数信息构造分段有理逼近函数；
关于解函数幂级数初等运算和初等函数规则如下：以一元幂函数为例，其他多元初等函数可仿照幂函数推导出规则。一元幂函数的一般形式为：
f(x(s))＝x n(s)
两边对s求导可得：
x(s)·[f′(x(s))·x′(s)]＝nf(x(s))·x′(s)
此时有：
Σ q≥0x[q]s q·Σ q≥0(q+1)f[q+1]s q＝nΣ q≥0f[q]s q·Σ q≥0(q+1)x[q+1]s q
这里的比较两边系数得到:
Figure PCTCN2022094899-appb-000033
此时可依次得到f[q]，也就得到了f(x(s))的幂级数展开式。
计算(DH(X(s))DH(X(s)) T) -1，记：
Figure PCTCN2022094899-appb-000034
Figure PCTCN2022094899-appb-000035
(11)式中两个矩阵满足：
Figure PCTCN2022094899-appb-000036
比较上式两边系数，可得以下线性方程组：
Figure PCTCN2022094899-appb-000037
Figure PCTCN2022094899-appb-000038
Figure PCTCN2022094899-appb-000039
也就是求解：
M[0]·Γ(:,j)[0]＝I j
这里，Γ(:,j)表示Γ的第j列，I j代表第j个数为1的列向量[0,0,…,1,…,0,0] T。
以及：
M[0]·Γ(:,j)[i]＝-U j
这里，U j的第j'个分量为
Figure PCTCN2022094899-appb-000040
通过求解Γ(s)各次对应幂级数系数矩阵的元素所组成的线性方程组，就能计算出(DH(X(s))DH(X(s)) T) -1。
将计算得到的f(X(s)),DH(X(s)),
Figure PCTCN2022094899-appb-000041
(DH(X(s))DH(X(s)) T) -1表达式，代入(9)式得到：
Figure PCTCN2022094899-appb-000042
比较s的同次幂系数得到：
Figure PCTCN2022094899-appb-000043
求解X[i+1]所满足的线性方程组，通过以下顺序：
Figure PCTCN2022094899-appb-000044
解出(10)中所有的幂级数系数。
S225、将分段有理逼近函数在s＝s'处的值代入微分动力***，即
Figure PCTCN2022094899-appb-000045
比较方程左右两边之差的模是否小于预设阈值e来判断幂级数是否在s'处收敛；
S226、若满足方程左右两边之差的模小于预设阈值e，扩大s'并返回步骤S225，找到尽可能大的且符合条件的s'；
S227、若不满足方程左右两边之差的模小于预设阈值e，缩小s'并返回步骤S225，直至方程左右两边之差的模小于预设阈值e；
具体地，将有理近似函数在s＝s 0处的值代入方程(5)，比较方程左右两边的差值是否小于预先设置的可容许的阈值e。若满足，则扩大s 0，直到不满足为止；若不满足，则缩小s 0，直到满足为止。即找到尽可能大的且小于阈值e的s 0。
S228、将X(s')作为新的起点X 0；
S229、循环步骤S223-S228，计算出由分段有理逼近函数表示的解函数X(s)和常数s *，其中s *使得
Figure PCTCN2022094899-appb-000046
成立，在允许误差范围内
Figure PCTCN2022094899-appb-000047
得到稳定平衡点的近似值X(s *)；
S2210、稳定平衡点的近似值X(s *)，就是最优潮流问题的局部最优解的近似值。
具体地，求出满足终止条件的有理近似函数X(s *)和s *后，X(s *)就是我们要求的稳定平衡点，有理论已经证明：稳定平衡点对应于原优化问题(2)的局部最优解,即：
Figure PCTCN2022094899-appb-000048
其中z *是对应于最优解x *的松弛变量。
进一步作为本方法的优选实施例，所述基于全局搜索对获得的多个局部最优解的近似值进行比较，得到近似全局最优解这一步骤，其具体包括：
S31、循环步骤S22直至达到预设次数，得到多个局部最优解；
S32、比较多个局部最优解，选取最小的局部最优解作为近似全局最优解。
具体地，运用全局搜索方法，重复步骤S22，通过比较多个局部最优解，选取最小的作为近似全局最优解，也就是对应于最优潮流问题的近似全局最优解，有：
Figure PCTCN2022094899-appb-000049
从而得到最优潮流调度方案：包含n b*1维的最优母线电压幅值
Figure PCTCN2022094899-appb-000050
和角度
Figure PCTCN2022094899-appb-000051
Figure PCTCN2022094899-appb-000052
维最优发电机有功功率
Figure PCTCN2022094899-appb-000053
和无功功率
Figure PCTCN2022094899-appb-000054
将它们代入目标函数
Figure PCTCN2022094899-appb-000055
可以得到目标函数的最优值
Figure PCTCN2022094899-appb-000056
通过以上步骤，我们解决了满足线路结构、线路传输最大电流或功率流以及母线可容许的电压范围等约束条件下的最优潮流问题。应用此方法，可以计算出经济效益和社会效益作为目标函数的最优发电节点配置方案，然后将最优的调度策略提供给电力***调度中心，从而使得电力***在安全可靠的前提下，尽可能多的降低发电成本，提高经济效益和社会效益。
本发明方法可以有效地克服传统方法中的计算难点，具体来说：在将最优潮流问题转化为求解常微分方程的初值问题的过程中，包含函数矩阵求逆的任务。需要注意的是，利用传统的方式求函数矩阵的逆，通常难以实现。我们通过FFHE方法可快速高效地计算出函数矩阵的逆矩阵中各个元素的幂级数，即将原矩阵和待求逆矩阵中各个元素上的函数展开成幂级数，利用上述两个矩阵相乘等于单位矩阵的性质，比较等式左右同类项系数，就可以计算出函数矩阵的逆矩阵中各个元素的幂级数。
本发明方法计算效率高，收敛速度快，具体来说：针对传统迭代优化方法和常微分方程 的传统计算方法，在求解上述最优潮流问题以及等价的动力***的过程中表现出的收敛慢等问题，我们利用FFHE方法的高精度逼近策略可进行大跨步地分段逼近，计算少量的中间过渡点就可以获得相应动力***的稳定平衡点的近似值,对应于最优潮流问题的局部最优解的近似值。
本发明方法在计算过程中节省大量存储空间，具体来说：在求解所构造的等价动力***过程中，基于传统迭代思想的龙格-库塔等方法需要存储大量中间点的函数值以近似刻画解曲线。相比之下，本方法只需计算少量的中间过渡点并存储各解函数关于变量的分段有理逼近函数各项系数和有效区间长度等信息，能节省大量存储空间。
本发明方法能高效地得到高精度的数值解，具体来说：基于FFHE的求解方法使用分段有理逼近方法构造解函数，相较于传统方法在数值计算中有更高的精度优势。此外，在数值仿真中，可将分段有理逼近函数选取为分段帕德逼近函数，仅需计算两个行列式，即可以得到帕德逼近函数在某处的值，相较于依次求解帕德逼近函数各项系数，有计算效率更高的优势。
本发明方法可运用经典的数学理论来确定解的误差上限，具体来说：基于FFHE的求解方法可以得到近似解的解析表达式，通过计算近似解的导数，代入原微分动力***可计算方程在左右两边之差，可以利用经典的数学理论严格地确定误差上界。
最优潮流在不同场合有不同应用功能，下表列出了几种最优潮流主要应用方向，本领域技术人员可以将本专利中的目标函数、控制变量、约束条件按具体应用问题进行变化、修改、替换、变形。
表1最优潮流在电力***下的不同应用
Figure PCTCN2022094899-appb-000057
以上是对本发明的较佳实施进行了具体说明，但本发明创造并不限于所述实施例，熟悉本领域的技术人员在不违背本发明精神的前提下还可做作出种种的等同变形或替换，这些等同的变形或替换均包含在本申请权利要求所限定的范围内。

Claims (5)

  1. 一种快速灵活全纯嵌入式电力***最优潮流评估方法，其特征在于，包括以下步骤：
    S1、获取电网数据并建立最优潮流计算模型；
    S2、基于最优潮流计算模型建立微分动力***并求解稳定平衡点的近似值，得到局部最优解的近似值；
    S3、基于全局搜索对获得的多个局部最优解的近似值进行比较，得到近似全局最优解；
    S4、根据近似全局最优解评估最优潮流调度方案。
  2. 根据权利要求1所述一种快速灵活全纯嵌入式电力***最优潮流评估方法，其特征在于，所述基于最优潮流计算模型建立微分动力***并求解稳定平衡点的近似值，得到局部最优解的近似值这一步骤，其具体包括：
    S21、根据最优潮流模型将最优潮流问题转化为等式约束的优化问题，建立等价的微分动力***；
    S22、基于分段有理逼近方法求解微分动力***稳定平衡点的近似值，得到最优潮流问题的局部最优解的近似值。
  3. 根据权利要求2所述一种快速灵活全纯嵌入式电力***最优潮流评估方法，其特征在于，所述微分动力***可表达如下：
    Figure PCTCN2022094899-appb-100001
    上式中，X为优化变量，s为嵌入变量，t为该动力***的时间变量，
    Figure PCTCN2022094899-appb-100002
    指目标函数的梯度在约束平面切空间上的正交投影。
  4. 根据权利要求3所述一种快速灵活全纯嵌入式电力***最优潮流评估方法，其特征在于，所述基于分段有理逼近方法求解微分动力***稳定平衡点的近似值，得到最优潮流问题的局部最优解的近似值这一步骤，其具体包括：
    S221、初始化参数，设定幂级数部分和的阶数q max，等式两边容许误差阈值e，最终停止误差阈值ε，找到任一可行点作为初始点X 0＝X(0)；
    S222、给出解函数向量X关于时间s的幂级数X(s)；
    S223、将幂级数X(s)代入微分动力***，得到以幂级数展开式系数为未知数的方程；
    S224、比较步骤S223中关于s的同次幂级数，并计算出X(s)的各项幂级数系数，根据幂级数信息构造分段有理逼近函数；
    S225、将分段有理逼近函数在s＝s'处的值代入微分动力***，即
    Figure PCTCN2022094899-appb-100003
    Figure PCTCN2022094899-appb-100004
    比较方程左右两边之差的模是否小于预设阈值e来判断幂级数是否在s'处收敛；
    S226、若满足方程左右两边之差的模小于预设阈值e，扩大s'并返回步骤S225，找到尽可能大的且符合条件的s'；
    S227、若不满足方程左右两边之差的模小于预设阈值e，缩小s'并返回步骤S225，直至方程左右两边之差的模小于预设阈值s；
    S228、将X(s')作为新的起点X 0；
    S229、循环步骤S223-S228，计算出由分段有理逼近函数表示的解函数X(s)和常数s *，其中s *使得
    Figure PCTCN2022094899-appb-100005
    成立，在允许误差范围内
    Figure PCTCN2022094899-appb-100006
    得到稳定平衡点的近似值X(s *)；
    S2210、稳定平衡点的近似值X(s *)，就是最优潮流问题的局部最优解的近似值。
  5. 根据权利要求4所述一种快速灵活全纯嵌入式电力***最优潮流评估方法，其特征在于，所述基于全局搜索对获得的多个局部最优解的近似值进行比较，得到近似全局最优解这一步骤，其具体包括：
    S31、循环步骤S2直至达到预设次数，得到多个局部最优解的近似值；
    S32、比较多个局部最优解的近似值，选取最小的局部最优解作的近似值为近似全局最优解。
PCT/CN2022/094899 2021-07-19 2022-05-25 一种快速灵活全纯嵌入式电力***最优潮流评估方法 WO2023000807A1 (zh)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN202110812483.5 2021-07-19
CN202110812483.5A CN113489014B (zh) 2021-07-19 2021-07-19 一种快速灵活全纯嵌入式电力***最优潮流评估方法

Publications (1)

Publication Number Publication Date
WO2023000807A1 true WO2023000807A1 (zh) 2023-01-26

Family

ID=77941181

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2022/094899 WO2023000807A1 (zh) 2021-07-19 2022-05-25 一种快速灵活全纯嵌入式电力***最优潮流评估方法

Country Status (2)

Country Link
CN (1) CN113489014B (zh)
WO (1) WO2023000807A1 (zh)

Families Citing this family (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113489014B (zh) * 2021-07-19 2023-06-02 中山大学 一种快速灵活全纯嵌入式电力***最优潮流评估方法
CN114336635B (zh) * 2022-01-05 2023-07-25 国网内蒙古东部电力有限公司通辽供电公司 基于常项值和先验节点的全纯嵌入潮流计算方法、装置
CN114548400A (zh) * 2022-02-10 2022-05-27 中山大学 一种快速灵活全纯嵌入式神经网络广域寻优训练方法
WO2024103221A1 (zh) * 2022-11-14 2024-05-23 中山大学 一种快速灵活全纯嵌入式电网越限预测及稳定性评估方法
CN115693688B (zh) * 2022-11-14 2023-09-15 中山大学 一种快速灵活全纯嵌入式电网越限预测及稳定性评估方法

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110739702A (zh) * 2019-09-17 2020-01-31 杭州电子科技大学 基于helm的配电网电压对变压器变比灵敏度计算方法
CN111082427A (zh) * 2020-01-07 2020-04-28 湘潭大学 一种基于全纯函数的微电网潮流计算方法
CN113489014A (zh) * 2021-07-19 2021-10-08 中山大学 一种快速灵活全纯嵌入式电力***最优潮流评估方法

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111130118B (zh) * 2020-01-09 2021-02-02 清华大学 一种基于分段线性化的电力***最优潮流计算方法
CN112952801B (zh) * 2021-02-04 2023-03-31 中山大学 一种基于快速灵活全纯嵌入思想的电网负荷裕度评估方法

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110739702A (zh) * 2019-09-17 2020-01-31 杭州电子科技大学 基于helm的配电网电压对变压器变比灵敏度计算方法
CN111082427A (zh) * 2020-01-07 2020-04-28 湘潭大学 一种基于全纯函数的微电网潮流计算方法
CN113489014A (zh) * 2021-07-19 2021-10-08 中山大学 一种快速灵活全纯嵌入式电力***最优潮流评估方法

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
CHIANG HSIAO-DONG; WANG TAO: "On the Existence of and Lower Bounds for the Number of Optimal Power Flow Solutions", IEEE TRANSACTIONS ON POWER SYSTEMS, IEEE, USA, vol. 34, no. 2, 1 March 2019 (2019-03-01), USA, pages 1116 - 1126, XP011710498, ISSN: 0885-8950, DOI: 10.1109/TPWRS.2018.2871067 *
FU HUANHUAN: "Static Voltage Stability Analysis of Islanded Microgrid Based on Holomorphic Embedding Method", CHINA MASTER'S' THESES FULL-TEXT DATABASE (ELECTRONIC JOURNAL)-INFORMATION & TECHNOLOGY), TIANJIN POLYTECHNIC UNIVERSITY, CN, 15 January 2021 (2021-01-15), CN , XP093026936, ISSN: 1674-0246 *
WANG, TAO ET AL.: ""Theoretical Study of Non-Iterative Holomorphic Embedding Methods for Solving Nonlinear Power Flow Equations: Algebraic Property"", IEEE TRANSACTIONS ON POWER SYSTEMS, vol. 36, no. 4, 3 December 2020 (2020-12-03), XP011861733, ISSN: 1558-0679, DOI: 10.1109/TPWRS.2020.3042283 *
YANG JIAN, WEI HUA, QIN XIUJUN: "Transient Stability Constrained Optimal Power Flow Based on Second-order Orthogonal Collocation Method", PROCEEDINGS OF THE CSEE, ZHONGGUO DIANJI GONGCHENG XUEHUI, CN, vol. 37, no. 1, 3 January 2017 (2017-01-03), CN , pages 64 - 73, XP093026937, ISSN: 0258-8013, DOI: 10.13334/j.0258-8013.pcsee.151451 *

Also Published As

Publication number Publication date
CN113489014B (zh) 2023-06-02
CN113489014A (zh) 2021-10-08

Similar Documents

Publication Publication Date Title
WO2023000807A1 (zh) 一种快速灵活全纯嵌入式电力***最优潮流评估方法
Zhang et al. A novel hybrid model for wind speed prediction based on VMD and neural network considering atmospheric uncertainties
CN108846517B (zh) 一种分位数概率性短期电力负荷预测集成方法
Yin et al. Joint identification of plant rational models and noise distribution functions using binary-valued observations
Colombino et al. Towards robustness guarantees for feedback-based optimization
CN111612147A (zh) 深度卷积网络的量化方法
CN113193556B (zh) 基于概率预测模型的短期风电功率预测方法
CN109314390B (zh) 获取直流电力网潮流的等量电导补偿型全局线性对称方法
CN108054757B (zh) 一种内嵌无功和电压的n-1闭环安全校核方法
CN109478781B (zh) 获取直流电力网功率传输系数的均衡电导补偿型对称方法
CN115453871A (zh) 一种基于ide扩展多维泰勒网的非线性***建模方法
CN113743806B (zh) 一种电力***非凸双目标最优潮流全局解的搜索方法
WO2018209479A1 (zh) 获取直流电力网潮流的无损耗全局线性偏心方法
CN110609468A (zh) 基于pi的非线性时滞多智能体***的一致性控制方法
Li et al. Strong predictor–corrector Euler–Maruyama methods for stochastic differential equations with Markovian switching
Xing et al. Hydrological time series forecast by ARIMA+ PSO-RBF combined model based on wavelet transform
CN109417291B (zh) 获取直流电力网潮流的均衡电导补偿型全局线性对称方法
CN109257947B (zh) 获取直流电力网功率传输系数的等量电导补偿型偏心方法
CN109257949B (zh) 获取直流电力网潮流的等量电导补偿型全局线性偏心方法
CN109257946B (zh) 获取直流电力网功率传输系数的无损耗偏心方法
CN115883408B (zh) 一种基于补偿的多速率复杂网络状态估计方法
CN109474258A (zh) 基于核极化策略的随机傅立叶特征核lms的核参数优化方法
WO2018209481A1 (zh) 获取直流电力网功率传输系数的无损耗对称方法
Ning et al. Robust decentralized H∞ control of multi-channel systems with norm-bounded parametric uncertainties
CN114936522B (zh) 一种天然气***动态建模方法

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 22844974

Country of ref document: EP

Kind code of ref document: A1

NENP Non-entry into the national phase

Ref country code: DE