WO2019174555A1 - 一种基于直算法的电力系统机电暂态仿真方法 - Google Patents

一种基于直算法的电力系统机电暂态仿真方法 Download PDF

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WO2019174555A1
WO2019174555A1 PCT/CN2019/077729 CN2019077729W WO2019174555A1 WO 2019174555 A1 WO2019174555 A1 WO 2019174555A1 CN 2019077729 W CN2019077729 W CN 2019077729W WO 2019174555 A1 WO2019174555 A1 WO 2019174555A1
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generator
sqi
sdi
frequency
power
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邓宏伟
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邓宏伟
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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
    • H02J3/001—Methods to deal with contingencies, e.g. abnormalities, faults or failures
    • H02J3/00125—Transmission line or load transient problems, e.g. overvoltage, resonance or self-excitation of inductive loads
    • 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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
    • 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
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation
    • 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
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • 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
    • Y04S40/00—Systems for electrical power generation, transmission, distribution or end-user application management characterised by the use of communication or information technologies, or communication or information technology specific aspects supporting them
    • Y04S40/20—Information technology specific aspects, e.g. CAD, simulation, modelling, system security

Definitions

  • the invention belongs to the technical field of power system simulation, and particularly relates to an electromechanical transient simulation method of a power system based on a straight algorithm.
  • Electromechanical transient simulation of power systems is a very important analytical method for power systems.
  • the running power system it can be predicted through simulation that under the large disturbance (such as short circuit fault, cut off line, generator, load, generator regulation excitation, impact load and transformer shift position, etc.) will not endanger the power system.
  • Safety whether the voltage of all busbars in the system is within the allowable range, whether the various components (such as lines, transformers, etc.) in the system will be overloaded, and what precautions should be taken before overload.
  • simulation can also be used to verify whether the proposed power system planning solution can meet the requirements of various operating modes.
  • the algorithm of electromechanical transient simulation of traditional power system is to solve the differential equations and algebraic equations of power system in series to obtain the time domain solution of physical quantities.
  • the methods for solving differential equations mainly include implicit trapezoidal integral method, improved Euler method and Runge-Kutta method.
  • the method of solving algebraic equations mainly adopts the Newton method, which is an iterative method, which is suitable for solving nonlinear algebraic equations.
  • the present invention aims to provide an electromechanical transient simulation method for a power system based on a straight algorithm, which overcomes the defects of the traditional simulation method, without iteration, fast calculation speed, high precision and small error. It truly reflects the changing characteristics of the grid. For example, the impedance of each line, load and transformer changes with the frequency of the grid. The frequency of each generator in the grid can also change dynamically according to its own laws.
  • the technical solution adopted by the invention is: a method for electromechanical transient simulation of a power system based on a straight algorithm, comprising the following steps:
  • A. Initialize power system parameters and calculate an initial matrix of each node in the power system
  • the output active power of the nth frame of the i-th generator is P i,n
  • the output reactive power is Q i,n
  • the generator terminal voltage is U i,n
  • the power factor is COS i,n ;
  • J i is the moment of inertia of the i-th node generator
  • ⁇ T is the frame calculation time interval
  • n is the frame number
  • the initial value of n is 0;
  • G the average frequency of the n+1th frame of all generators on the grid Substituting the n+1th frame frequency of the power grid, where m is the total number of generators in the power system;
  • initializing the power system parameters in step A specifically includes the following process:
  • A5. Set the dynamic torque of the grid-connected generator, or share the load of the whole network according to the capacity ratio of the grid-connected generator, and determine the first frame and the initial frame dynamic torque of each generator.
  • the initial load matrix is:
  • the initial line matrix is:
  • the initial matrix of the transformer is:
  • the generator initial matrix is:
  • step H the specific process of calculating the reactance and susceptance of each node according to f W,n+1 is as follows:
  • the reactance per kilometer of the line at the frequency f W,n+1 is The kilowatt hour per kilometer.
  • the reactance of the transformer at the frequency f W,n+1 is Density
  • step H the new matrix of each node at the frequency f W,n+1 is as follows:
  • the new load matrix is:
  • the new line matrix is:
  • the new matrix of transformers is:
  • the new generator matrix is:
  • T i,n+1 T i,n -K Ti ⁇ [f i,n+1 -(50+ ⁇ f sqi )];
  • T i,n+1 T i,n +K Ti ⁇ [(50- ⁇ f sqi )-f i,n+1 ];
  • T i,n+1 T i,n ;
  • K Ti is the frequency modulation factor and ⁇ f sqi is the dead zone frequency.
  • the excitation adjustment of the generator can only be selected from one of four types: no adjustment, voltage adjustment, reactive power adjustment, and power factor adjustment:
  • I Li,n+1 I Li,n -K ui ⁇ [U i,n -(U sdi + ⁇ U sqi )];
  • I Li,n+1 I Li,n +K ui ⁇ [(U sdi - ⁇ U sqi )-U i,n ];
  • I Li,n+1 I Li,n -K Qi ⁇ [Q i,n -(Q sdi + ⁇ Q sqi )];
  • I Li,n+1 I Li,n +K Qi ⁇ [(Q sdi - ⁇ Q sqi )-Q i,n ];
  • I Li,n+1 I Li,n +K COSi ⁇ [COS i,n -(COS sdi + ⁇ COS sqi )];
  • K ui is the voltage regulation coefficient of the generator
  • U sdi is the set voltage
  • ⁇ U sqi is the dead zone voltage
  • U i,n is the nth frame port voltage of the i-th generator
  • K Qi is the reactive power of the generator
  • the adjustment factor, Q sdi is to set the reactive power
  • ⁇ Q sqi is the dead zone reactive power
  • Q i,n is the nth frame output reactive power of the i-th node generator
  • K COSi is the power factor adjustment coefficient of the generator.
  • COS sdi is the set power factor
  • ⁇ COS sqi is the dead zone power factor
  • COS i,n is the nth frame power factor of the i-th node generator.
  • This simulation method uses frame as the calculation unit, and it is repeatedly calculated one frame at a time. This calculation method has no end, and each frame has an output result. Mathematically, when the angular acceleration of all generators is zero, the flow is considered to be steady; in engineering applications, when the results of the last two frames are small (except for the angles of voltage and current), the flow can be considered stable. state.
  • parameters can be modified during calculation to simulate various disturbances in the power grid to change the power flow. If the Y value of the load is modified, the influence of the load change on the power grid can be simulated; the transformer n n , 1 , n i, 2 can be modified to simulate the on-load voltage regulation of the transformer; the excitation current of the generator can be modified to simulate the excitation of the generator.
  • This simulation method overcomes the defects of the traditional simulation method, without iteration, fast calculation speed, high precision and small error, which truly reflects the changing characteristics of the power grid, such as the impedance of each line, load and transformer with the frequency of the power grid. Changes in frequency, the frequency of each generator in the grid can also dynamically change according to their respective laws.
  • 1 is a flow chart of a method for electromechanical transient simulation of a power system based on a straight algorithm.
  • the technical solution adopted by the present invention is: a method for electromechanical transient simulation of a power system based on a straight algorithm, comprising the following steps:
  • A. Initialize power system parameters and calculate an initial matrix of each node in the power system
  • the straight algorithm calculates the power system power flow distribution as the prior art, please refer to the applicant's patent CN201410142938.7 and the patent application CN201610783305.3;
  • J i is the moment of inertia of the i-th node generator
  • ⁇ T is the frame calculation time interval
  • n is the frame number
  • the initial value of n is 0;
  • G the average frequency of the n+1th frame of all generators on the grid (where m is the total number of generators in the power system) instead of the n+1th frame frequency of the grid;
  • initializing the power system parameters in step A specifically includes the following process:
  • A5. Set the dynamic torque of the grid-connected generator, or share the load of the whole network according to the capacity ratio of the grid-connected generator, and determine the first frame and the initial frame dynamic torque of each generator.
  • the reactance per kilometer is x i,0
  • the conductance per kilometer is g i,0
  • the wattage per kilometer is b i,0 and the length of the line is l i
  • the conductance of the transformer is Gt i,0
  • electricity The current is Bt i,0
  • the resistance is Rt i,0
  • the reactance is Xt i,0
  • the primary number of turns is n i,1 and the number of secondary sides is n i,2
  • the internal resistance of the generator is r′ i , 0 and reactance are x' i, 0 ; then the initial matrix of each node is as follows:
  • the initial load matrix is:
  • the initial line matrix is:
  • the initial matrix of the transformer is:
  • the generator initial matrix is:
  • R i,0 50 Hz
  • R i,0 X i,0 , r i,0 , x i,0 , g i,0 , b i,0 , Gt i,0 ,Bt i,0
  • the values of Rt i,0 , Xt i,0 , r′ i,0 and x′ i,0 can be determined, and for specific conditions, specific values are brought into the corresponding initial matrix.
  • step H the specific process of calculating the reactance and susceptance of each node according to f W,n+1 is as follows:
  • the reactance per kilometer of the line at the frequency f W,n+1 is The kilowatt hour per kilometer.
  • the reactance of the transformer at the frequency f W,n+1 is Density
  • step H the new matrix of each node at the frequency f W,n+1 is as follows:
  • the new load matrix is:
  • the new line matrix is: among them:
  • the new matrix of transformers is:
  • the new generator matrix is:
  • T i,n+1 T i,n ;
  • the generator is a frequency modulation generator, then there are:
  • T i,n+1 T i,n -K Ti ⁇ [f i,n+1 -(50+ ⁇ f sqi )];
  • T i,n+1 T i,n +K Ti ⁇ [(50- ⁇ f sqi )-f i,n+1 ];
  • T i,n+1 T i,n ;
  • K Ti is the frequency modulation factor and ⁇ f sqi is the dead zone frequency.
  • the excitation adjustment of the generator can only be selected from one of four types: no adjustment, voltage adjustment, reactive power adjustment, and power factor adjustment:
  • I Li,n+1 I Li,n -K ui ⁇ [U i,n -(U sdi + ⁇ U sqi )];
  • I Li,n+1 I Li,n +K ui ⁇ [(U sdi - ⁇ U sqi )-U i,n ];
  • I Li,n+1 I Li,n -K Qi ⁇ [Q i,n -(Q sdi + ⁇ Q sqi )];
  • I Li,n+1 I Li,n +K Qi ⁇ [(Q sdi - ⁇ Q sqi )-Q i,n ];
  • I Li,n+1 I Li,n +K COSi ⁇ [COS i,n -(COS sdi + ⁇ COS sqi )];
  • K ui is the voltage regulation coefficient of the generator
  • U sdi is the set voltage
  • ⁇ U sqi is the dead zone voltage
  • U i,n is the nth frame port voltage of the i-th generator
  • K Qi is the reactive power of the generator
  • the adjustment factor, Q sdi is to set the reactive power
  • ⁇ Q sqi is the dead zone reactive power
  • Q i,n is the nth frame output reactive power of the i-th node generator
  • K COSi is the power factor adjustment coefficient of the generator.
  • COS sdi is the set power factor
  • ⁇ COS sqi is the dead zone power factor
  • COS i,n is the nth frame power factor of the i-th node generator.

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  • Engineering & Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Power Engineering (AREA)
  • Physics & Mathematics (AREA)
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Abstract

本发明公开了一种基于直算法的电力系统机电暂态仿真方法，包括以下步骤：A初始化电力系统参数；B采用直算法计算电力系统潮流分布；C计算每台发电机下一帧角加速度、角速度、转子角度、频率；D进行频率调节；E进行励磁调节；F根据发电机下一帧转子角度和频率计算发电机旋转电动势；G根据每台发电机的频率fi,n+1，计算全网的平均频率fW,n+1；H将平均频率fW,n+1带入每一个节点并计算其相应的电抗和电纳，并将旋转电动势代入到相应的发电机中，最后计算得出所有节点的新矩阵；I重新进入步骤B。本发明克服了传统仿真法的缺陷，无迭代、计算速度快、精度高且误差小，真实地反映了电网的变化特性。

Description

一种基于直算法的电力系统机电暂态仿真方法 技术领域
本发明属于电力系统仿真技术领域，具体涉及基于直算法的电力系统机电暂态仿真方法。
背景技术
电力系统机电暂态仿真是电力系统非常重要的分析方法。对运行中的电力系统，通过仿真可以预知在大扰动下(如短路故障、切除线路、发电机、负载、发电机调节励磁、冲击性负载以及变压器调档位等)会不会危及电力系统的安全，系统中所有母线的电压是否在允许的范围以内，系统中各种元件(如线路、变压器等)是否会出现过负载，以及可能出现过负载时应事先采取哪些预防措施。对规划中的电力系统，也可通过仿真来检验所提出的电力系统规划方案能否满足各种运行方式的要求。
传统电力系统机电暂态仿真的算法是联立求解电力系统微分方程组和代数方程组，以获得物理量的时域解。微分方程组的求解方法主要有隐式梯形积分法、改进尤拉法和龙格-库塔法等。代数方程组的求解法主要采用适用于求解非线性代数方程组的牛顿法，即迭代法。
传统机电暂态仿真方法的缺陷是计算结果误差大、精度低以及速度慢、还时常不收敛；且其建立在所有发电机的频率是同步一致的基础之上，这与电网的实际情况不符，难以反映电网的真实变化。
发明内容
为了解决现有技术存在的上述问题，本发明目的在于提供一种基于直算法的电力系统机电暂态仿真方法，其克服了传统仿真法的缺陷，无迭代、计算速度快、精度高且误差小，真实地反映了电网的变化特性，如各线路、负载和变压器的阻抗随着电网的频率变化而变化，电网中各发电机的频率也能按各自的 规律动态地变化。
本发明所采用的技术方案为：一种基于直算法的电力系统机电暂态仿真方法，包括以下步骤：
A、初始化电力系统参数，计算电力系统中各节点初始矩阵；
B、采用直算法计算电力系统潮流分布，其中第i节点发电机第n帧的输出有功功率为P i,n、输出无功功率为Q i,n、发电机端电压为U i,n和功率因数为COS i,n；
C、进行频率调节，调节第i节点发电机第n+1帧动力矩T i,n+1；
D、进行励磁调节，调节第i节点发电机第n+1帧励磁电流I Li,n+1；
E、计算第i节点发电机的第n+1帧角加速度
Figure PCTCN2019077729-appb-000001
角速度ω i,n+1、转子角度θ i,n+1和频率f i,n+1：
Figure PCTCN2019077729-appb-000002
其中，J i是第i节点发电机的转动惯量，ΔT是帧计算时间间隔，n是帧序号，n的初始值为0；
F、根据发电机第n+1帧的转子角度θ i,n+1、频率f i,n+1以及励磁电流I Li,n+1，计算发电机的第n+1帧旋转电动势：
发电机旋转电动势的绝对值|E i,n+1|＝K Li×I Li,n+1×f i,n+1，则旋转电动势向量值
Figure PCTCN2019077729-appb-000003
其中K Li是i节点发电机的电动势系数；
G、用电网上所有发电机第n+1帧的平均频率
Figure PCTCN2019077729-appb-000004
代替电网的第n+1帧频率，其中m为电力系统中发电机的总数量；
H、根据f W,n+1计算各节点的电抗和电纳，将
Figure PCTCN2019077729-appb-000005
以及计算得到的各节点的电抗和电纳带入到各节点的初始矩阵中，最后计算得出各节点的新矩阵；
I、重新进入步骤B。
进一步地，步骤A中初始化电力系统参数具体包括如下过程：
A1、设置帧计算时间间隔ΔT；
A2、设置每台发电机的初始频率f i,0＝50Hz，初始角加速度
Figure PCTCN2019077729-appb-000006
初始角度θ i,0＝0，初始角速度ω i,0＝2×π×f i,0；
A3、设置每台发电机的励磁电流I Li,0为额定值以及励磁系数K Li，则其旋转电动势初始值
Figure PCTCN2019077729-appb-000007
A4、设网上系统频率初始值为f W,0＝50Hz,根据f W,0确定每一个节点的电抗和电纳，最后计算出所有节点的初始矩阵；
A5、设置并网发电机的动力矩，或按并网发电机的容量占比分摊全网负载，确定每台发电机的第1帧和起始帧动力矩
Figure PCTCN2019077729-appb-000008
A6、设置调频发电机的调频系数K Ti和死区频率Δf sqi；
A7、设置电压调节发电机的电压调节系数K ui、设置电压U sdi和死区电压ΔU sqi；
A8、设置无功调节发电机的无功调节系数K Qi、设置无功功率Q sdi和死区无功功率ΔQ sqi；
A9、设置功率因数调节发电机的功率因数调节系数K cosi、设置功率因数COS sdi和死区功率因数ΔCOS sqi。
进一步地，步骤A4具体包括以下过程：设电力系统中，在初始频率f W,0＝50Hz时，负载的电阻为R i,0和电抗为X i,0；线路每公里电阻为r i,0、每公里电抗为x i,0、每公里电导为g i,0、每公里电纳为b i,0和线路长度为l i；变压器的电导为Gt i,0、电纳为Bt i,0、电阻为Rt i,0、电抗为Xt i,0，原边匝数为n i,1和副边匝数为n i,2；发电机的 内阻为r′ i,0和电抗为x′ i,0；则各节点初始矩阵如下：
负载初始矩阵为：
Figure PCTCN2019077729-appb-000009
线路初始矩阵为：
Figure PCTCN2019077729-appb-000010
其中，z i,0＝r i,0+jx i,0，y i,0＝g i,0+jb i,0，
Figure PCTCN2019077729-appb-000011
变压器初始矩阵为：
Figure PCTCN2019077729-appb-000012
发电机初始矩阵为：
Figure PCTCN2019077729-appb-000013
进一步地，步骤H中，根据f W,n+1计算各节点的电抗和电纳的具体过程如下：
负载在频率f W,n+1下的电抗为
Figure PCTCN2019077729-appb-000014
线路在频率f W,n+1下的每公里电抗为
Figure PCTCN2019077729-appb-000015
每公里电纳为
Figure PCTCN2019077729-appb-000016
变压器在频率f W,n+1下的电抗为
Figure PCTCN2019077729-appb-000017
电纳为
Figure PCTCN2019077729-appb-000018
发电机在频率f W,n+1下的电抗为
Figure PCTCN2019077729-appb-000019
进一步地，步骤H中，各节点在频率f W,n+1下的新矩阵如下：
负载新矩阵为：
Figure PCTCN2019077729-appb-000020
线路新矩阵为：
Figure PCTCN2019077729-appb-000021
其中，z i,n+1＝r i,0+jx i,n+1，y i,n+1＝g i,0+jb i,n+1，
Figure PCTCN2019077729-appb-000022
变压器新矩阵为：
Figure PCTCN2019077729-appb-000023
发电机新矩阵为：
Figure PCTCN2019077729-appb-000024
进一步地，所述步骤C中进行频率调节时，若发电机是非调频发电机，则有：T i,n+1＝T i,n；若发电机是调频发电机，则有：
当f i,n+1>50+Δf sqi时，T i,n+1＝T i,n-K Ti×[f i,n+1-(50+Δf sqi)]；
当f i,n+1<50-Δf sqi时，T i,n+1＝T i,n+K Ti×[(50-Δf sqi)-f i,n+1]；
当f i,n+1≥50-Δf sqi且f i,n+1≤50+Δf sqi时，T i,n+1＝T i,n；
其中，K Ti是调频系数，Δf sqi是死区频率。
进一步地，所述步骤D中进行励磁调节时，发电机的励磁调节只能在不调节、电压调节、无功调节和功率因数调节这四种之中选择一种：
若发电机不参与励磁调节，则I Li,n+1＝I Li,n；
若是电压调节发电机，则有：
当U i,n>U sdi+ΔU sqi时，I Li,n+1＝I Li,n-K ui×[U i,n-(U sdi+ΔU sqi)]；
当U i,n<U sdi-ΔU sqi时，I Li,n+1＝I Li,n+K ui×[(U sdi-ΔU sqi)-U i,n]；
当U i,n≥U sdi-ΔU sqi且U i,n≤U sdi+ΔU sqi时，I Li,n+1＝I Li,n；
若是无功调节发电机，则有：
当Q i,n>Q sdi+ΔQ sqi时，I Li,n+1＝I Li,n-K Qi×[Q i,n-(Q sdi+ΔQ sqi)]；
当Q i,n<Q sdi-ΔQ sqi时，I Li,n+1＝I Li,n+K Qi×[(Q sdi-ΔQ sqi)-Q i,n]；
当Q i,n≥Q sdi-ΔQ sqi且Q i,n≤Q sdi+ΔQ sqi时，I Li,n+1＝I Li,n；
若是功率因数调节发电机，则有：
当COS i,n>COS sdi+ΔCOS sqi时，I Li,n+1＝I Li,n+K COSi×[COS i,n-(COS sdi+ΔCOS sqi)]；
当COS i,n<COS sdi-ΔCOS sqi时，I Li,n+1＝I Li,n-K COSi×[(COS sdi-ΔCOS sqi)-COS i,n]；
当COS i,n≥COS sdi-ΔCOS sqi且COS i,n≤COS sdi+ΔCOS sqi时，I Li,n+1＝I Li,n；
其中，K ui是发电机的电压调节系数，U sdi是设定电压，ΔU sqi是死区电压，U i,n是第i节点发电机第n帧端口电压，K Qi是发电机的无功调节系数，Q sdi是设定无功功率，ΔQ sqi是死区无功功率，Q i,n是第i节点发电机第n帧输出无功功率，K COSi是发电机的功率因数调节系数，COS sdi是设定功率因数，ΔCOS sqi是死区功率 因数，COS i,n是第i节点发电机第n帧功率因数。
本发明的有益效果为：
(1)本仿真方法以帧为计算单位，一帧一帧不断重复地计算，此计算方法没有终结，每一帧都有输出结果。在数学上当所有发电机的角加速度为零时，即认为潮流进入稳态；在工程应用方面，当前后两帧计算的结果相差较小时(电压和电流的辐角除外)，可认为潮流进入稳态。
(2)每帧计算的值即为机电暂态过程的中间值。
(3)采用这种计算方式，可在计算时修改参数，模仿电网中的各种扰动，使潮流发生变化。如修改负载的Y值，可仿真负载变化对电网的影响；修改变压器的n i,1、n i,2,可仿真变压器的有载调压；修改发电机的励磁电流，可仿真发电机励磁改变后的电网变化过程；修改发电机的动力矩，可仿真发电机出力变化对电网的影响；若将线路分成两段，在中间插入负载，令负载的Y＝0，则是正常线路，若令负载Y＝10000，则可以仿真线路短路。
(4)本仿真法克服了传统仿真法的缺陷，无迭代、计算速度快、精度高且误差小，真实地反映了电网的变化特性，如各线路、负载和变压器的阻抗随着电网的频率变化而变化，电网中各发电机的频率也能按各自的规律动态地变化。
附图说明
图1是基于直算法的电力系统机电暂态仿真方法的流程图。
具体实施方式
下面结合附图及具体实施例对本发明做进一步阐释。
实施例
如图1所示，本发明所采用的技术方案为：一种基于直算法的电力系统机电暂态仿真方法，包括以下步骤：
A、初始化电力系统参数，计算电力系统中各节点初始矩阵；
B、采用直算法计算电力系统潮流分布，其中第i节点发电机第n帧的输出有功功率为P i,n、输出无功功率为Q i,n、发电机端电压为U i,n和功率因数为COS i,n；直算法计算电力系统潮流分布为现有技术，请参考申请人的专利CN201410142938.7以及专利申请CN201610783305.3；
C、进行频率调节，调节第i节点发电机第n+1帧动力矩T i,n+1；
D、进行励磁调节，调节第i节点发电机第n+1帧励磁电流I Li,n+1；
E、计算第i节点发电机的第n+1帧角加速度
Figure PCTCN2019077729-appb-000025
角速度ω i,n+1、转子角度θ i,n+1和频率f i,n+1：
Figure PCTCN2019077729-appb-000026
其中，J i是第i节点发电机的转动惯量，ΔT是帧计算时间间隔，n是帧序号，n的初始值为0；
F、根据发电机第n+1帧的转子角度θ i,n+1、频率f i,n+1以及励磁电流I Li,n+1，计算发电机的第n+1帧旋转电动势：
发电机旋转电动势的绝对值|E i,n+1|＝K Li×I Li,n+1×f i,n+1，则旋转电动势向量值
Figure PCTCN2019077729-appb-000027
其中K Li是i节点发电机的电动势系数；
G、用电网上所有发电机第n+1帧的平均频率
Figure PCTCN2019077729-appb-000028
(其中m为电力系统中发电机的总数量)代替电网的第n+1帧频率；
H、根据f W,n+1计算各节点的电抗和电纳，将
Figure PCTCN2019077729-appb-000029
以及计算得到的各节点的电抗和电纳带入到各节点的初始矩阵中，最后计算得出各节点的新矩阵；
I、重新进入步骤B。
在另一实施例中，步骤A中初始化电力系统参数具体包括如下过程：
A1、设置帧计算时间间隔ΔT；
A2、设置每台发电机的初始频率f i,0＝50Hz，初始角加速度
Figure PCTCN2019077729-appb-000030
初始角度θ i,0＝0，初始角速度ω i,0＝2×π×f i,0；
A3、设置每台发电机的励磁电流I Li,0为额定值以及励磁系数K Li，则其旋转电动势
Figure PCTCN2019077729-appb-000031
A4、设网上系统频率初始值为f W,0＝50Hz,根据f W,0确定每一个节点的电抗和电纳，最后计算得出所有节点的初始矩阵；
A5、设置并网发电机的动力矩，或按并网发电机的容量占比分摊全网负载，确定每台发电机的第1帧和起始帧动力矩
Figure PCTCN2019077729-appb-000032
A6、设置调频发电机的调频系数K Ti和死区频率Δf sqi；
A7、设置电压调节发电机的电压调节系数K ui、设置电压U sdi和死区电压ΔU sqi；
A8、设置无功调节发电机的无功调节系数K Qi、设置无功功率Q sdi和死区无功功率ΔQ sqi；
A9、设置功率因数调节发电机的功率因数调节系数K cosi、设置功率因数COS sdi和死区功率因数ΔCOS sqi。
在另一实施例中，步骤A4具体包括以下过程：设电力系统中，在初始频率f W,0＝50Hz时，负载的电阻为R i,0和电抗为X i,0；线路每公里电阻为r i,0、每公里电抗为x i,0、每公里电导为g i,0、每公里电纳为b i,0和线路长度为l i；变压器的电导为Gt i,0、电纳为Bt i,0、电阻为Rt i,0、电抗为Xt i,0、原边匝数为n i,1和副边匝数为n i,2；发电机的内阻为r′ i,0和电抗为x′ i,0；则各节点初始矩阵如下：
负载初始矩阵为：
Figure PCTCN2019077729-appb-000033
线路初始矩阵为：
Figure PCTCN2019077729-appb-000034
其中，z i,0＝r i,0+jx i,0，y i,0＝g i,0+jb i,0，
Figure PCTCN2019077729-appb-000035
变压器初始矩阵为：
Figure PCTCN2019077729-appb-000036
发电机初始矩阵为：
Figure PCTCN2019077729-appb-000037
在初始频率f W,0＝50Hz时，R i,0、X i,0、r i,0、x i,0、g i,0、b i,0、Gt i,0、Bt i,0、Rt i,0、Xt i,0、r′ i,0和x′ i,0的值可确定，为已知条件，将具体值带入相应初始矩阵。
在另一实施例中，步骤H中，根据f W,n+1计算各节点的电抗和电纳的具体过程如下：
负载在频率f W,n+1下的电抗为
Figure PCTCN2019077729-appb-000038
线路在频率f W,n+1下的每公里电抗为
Figure PCTCN2019077729-appb-000039
每公里电纳为
Figure PCTCN2019077729-appb-000040
变压器在频率f W,n+1下的电抗为
Figure PCTCN2019077729-appb-000041
电纳为
Figure PCTCN2019077729-appb-000042
发电机在频率f W,n+1下的电抗为
Figure PCTCN2019077729-appb-000043
在另一实施例中，步骤H中，各节点在频率f W,n+1下的新矩阵如下：
负载新矩阵为：
Figure PCTCN2019077729-appb-000044
线路新矩阵为：
Figure PCTCN2019077729-appb-000045
其中：
Figure PCTCN2019077729-appb-000046
变压器新矩阵为：
Figure PCTCN2019077729-appb-000047
发电机新矩阵为：
Figure PCTCN2019077729-appb-000048
在另一实施例中，所述步骤C中进行频率调节时，
若发电机是非调频发电机，则T i,n+1＝T i,n；
若发电机是调频发电机，则有：
当f i,n+1>50+Δf sqi时，T i,n+1＝T i,n-K Ti×[f i,n+1-(50+Δf sqi)]；
当f i,n+1<50-Δf sqi时，T i,n+1＝T i,n+K Ti×[(50-Δf sqi)-f i,n+1]；
当f i,n+1≥50-Δf sqi且f i,n+1≤50+Δf sqi时，T i,n+1＝T i,n；
其中，K Ti是调频系数，Δf sqi是死区频率。
在另一实施例中，所述步骤D中进行励磁调节时，发电机的励磁调节只能在不调节、电压调节、无功调节和功率因数调节这四种之中选择一种：
若发电机不参与励磁调节，则I Li,n+1＝I Li,n；
若是电压调节发电机，则有：
当U i,n>U sdi+ΔU sqi时，I Li,n+1＝I Li,n-K ui×[U i,n-(U sdi+ΔU sqi)]；
当U i,n<U sdi-ΔU sqi时，I Li,n+1＝I Li,n+K ui×[(U sdi-ΔU sqi)-U i,n]；
当U i,n≥U sdi-ΔU sqi且U i,n≤U sdi+ΔU sqi时，I Li,n+1＝I Li,n；
若是无功调节发电机，则有：
当Q i,n>Q sdi+ΔQ sqi时，I Li,n+1＝I Li,n-K Qi×[Q i,n-(Q sdi+ΔQ sqi)]；
当Q i,n<Q sdi-ΔQ sqi时，I Li,n+1＝I Li,n+K Qi×[(Q sdi-ΔQ sqi)-Q i,n]；
当Q i,n≥Q sdi-ΔQ sqi且Q i,n≤Q sdi+ΔQ sqi时，I Li,n+1＝I Li,n；
若是功率因数调节发电机，则有：
当COS i,n>COS sdi+ΔCOS sqi时，I Li,n+1＝I Li,n+K COSi×[COS i,n-(COS sdi+ΔCOS sqi)]；
当COS i,n<COS sdi-ΔCOS sqi时，I Li,n+1＝I Li,n-K COSi×[(COS sdi-ΔCOS sqi)-COS i,n]；
当COS i,n≥COS sdi-ΔCOS sqi且COS i,n≤COS sdi+ΔCOS sqi时，I Li,n+1＝I Li,n；
其中，K ui是发电机的电压调节系数，U sdi是设定电压，ΔU sqi是死区电压，U i,n是第i节点发电机第n帧端口电压，K Qi是发电机的无功调节系数，Q sdi是设定无功功率，ΔQ sqi是死区无功功率，Q i,n是第i节点发电机第n帧输出无功功率，K COSi是发电机的功率因数调节系数，COS sdi是设定功率因数，ΔCOS sqi是死区功率因数，COS i,n是第i节点发电机第n帧功率因数。
本发明不局限于上述可选的实施方式，任何人在本发明的启示下都可得出其他各种形式的产品。上述具体实施方式不应理解成对本发明的保护范围的限制，本发明的保护范围应当以权利要求书中界定的为准，并且说明书可以用于解释权利要求书。

Claims (7)

  1. 一种基于直算法的电力系统机电暂态仿真方法，其特征在于，包括以下步骤：
    A、初始化电力系统参数，计算电力系统中各节点初始矩阵；
    B、采用直算法计算电力系统潮流分布，其中第i节点发电机第n帧的输出有功功率为P i,n、输出无功功率为Q i,n、发电机端电压为U i,n和功率因数为COS i,n；
    C、进行频率调节，调节第i节点发电机第n+1帧动力矩T i,n+1；
    D、进行励磁调节，调节第i节点发电机第n+1帧励磁电流I Li,n+1；
    E、计算第i节点发电机的第n+1帧角加速度
    Figure PCTCN2019077729-appb-100001
    角速度ω i,n+1、转子角度θ i,n+1和频率f i,n+1：
    Figure PCTCN2019077729-appb-100002
    其中，J i是第i节点发电机的转动惯量，ΔT是帧计算时间间隔，n是帧序号，n的初始值为0；
    F、根据发电机第n+1帧的转子角度θ i,n+1、频率f i,n+1以及励磁电流I Li,n+1，计算发电机的第n+1帧旋转电动势：
    发电机旋转电动势的绝对值|E i,n+1|＝K Li×I Li,n+1×f i,n+1，则旋转电动势向量值
    Figure PCTCN2019077729-appb-100003
    其中K Li是i节点发电机的电动势系数；
    G、用电网上所有发电机第n+1帧的平均频率
    Figure PCTCN2019077729-appb-100004
    代替电网的第n+1帧频率，其中m为电力系统中发电机的总数量；
    H、根据f W,n+1计算各节点的电抗和电纳，将
    Figure PCTCN2019077729-appb-100005
    以及计算得到的各节点的电 抗和电纳带入到各节点的初始矩阵中，最后计算得出各节点的新矩阵；
    I、重新进入步骤B。
  2. 根据权利要求1所述的基于直算法的电力系统机电暂态仿真方法，其特征在于，步骤A中初始化电力系统参数具体包括如下过程：
    A1、设置帧计算时间间隔ΔT；
    A2、设置每台发电机的初始频率f i,0＝50Hz，初始角加速度
    Figure PCTCN2019077729-appb-100006
    初始角度θ i,0＝0，初始角速度ω i,0＝2×π×f i,0；
    A3、设置每台发电机的励磁电流I Li,0为额定值以及励磁系数K Li，则其旋转电动势初始值
    Figure PCTCN2019077729-appb-100007
    A4、设网上系统频率初始值为f W,0＝50Hz,根据f W,0确定每一个节点的电抗和电纳，最后计算出所有节点的初始矩阵；
    A5、设置并网发电机的动力矩，或按并网发电机的容量占比分摊全网负载，确定每台发电机的第1帧和起始帧动力矩
    Figure PCTCN2019077729-appb-100008
    A6、设置调频发电机的调频系数K Ti和死区频率Δf sqi；
    A7、设置电压调节发电机的电压调节系数K ui、设置电压U sdi和死区电压ΔU sqi；
    A8、设置无功调节发电机的无功调节系数K Qi、设置无功功率Q sdi和死区无功功率ΔQ sqi；
    A9、设置功率因数调节发电机的功率因数调节系数K cosi、设置功率因数COS sdi和死区功率因数ΔCOS sqi。
  3. 根据权利要求2所述的基于直算法的电力系统机电暂态仿真方法，其特征在于，步骤A4具体包括以下过程：设电力系统中，在初始频率f W,0＝50Hz时，负载的电阻为R i,0和电抗为X i,0；线路每公里电阻为r i,0、每公里电抗为x i,0、每公里电导为g i,0、每公里电纳为b i,0和线路长度为l i；变压器的电导为Gt i,0、电纳为 Bt i,0、电阻为Rt i,0、电抗为Xt i,0，原边匝数为n i,1和副边匝数为n i,2；发电机的内阻为r′ i,0和电抗为x′ i,0；则各节点初始矩阵如下：
    负载初始矩阵为：
    Figure PCTCN2019077729-appb-100009
    线路初始矩阵为：
    Figure PCTCN2019077729-appb-100010
    其中，z i,0＝r i,0+jx i,0，y i,0＝g i,0+jb i,0，
    Figure PCTCN2019077729-appb-100011
    变压器初始矩阵为：
    Figure PCTCN2019077729-appb-100012
    发电机初始矩阵为：
    Figure PCTCN2019077729-appb-100013
  4. 根据权利要求3所述的基于直算法的电力系统机电暂态仿真方法，其特征在于，步骤H中，根据f W,n+1计算各节点的电抗和电纳的具体过程如下：
    负载在频率f W,n+1下的电抗为
    Figure PCTCN2019077729-appb-100014
    线路在频率f W,n+1下的每公里电抗为
    Figure PCTCN2019077729-appb-100015
    每公里电纳为
    Figure PCTCN2019077729-appb-100016
    变压器在频率f W,n+1下的电抗为
    Figure PCTCN2019077729-appb-100017
    电纳为
    Figure PCTCN2019077729-appb-100018
    发电机在频率f W,n+1下的电抗为
    Figure PCTCN2019077729-appb-100019
  5. 根据权利要求4所述的基于直算法的电力系统机电暂态仿真方法，其特征在于，步骤H中，各节点在频率f W,n+1下的新矩阵如下：
    负载新矩阵为：
    Figure PCTCN2019077729-appb-100020
    线路新矩阵为：
    Figure PCTCN2019077729-appb-100021
    其中，z i,n+1＝r i,0+jx i,n+1，y i,n+1＝g i,0+jb i,n+1，
    Figure PCTCN2019077729-appb-100022
    变压器新矩阵为：
    Figure PCTCN2019077729-appb-100023
    发电机新矩阵为：
    Figure PCTCN2019077729-appb-100024
  6. 根据权利要求2所述的基于直算法的电力系统机电暂态仿真方法，其特征在于，所述步骤C中进行频率调节时，
    若发电机是非调频发电机，则有：T i,n+1＝T i,n；
    若发电机是调频发电机，则有：
    当f i,n+1>50+Δf sqi时，T i,n+1＝T i,n-K Ti×[f i,n+1-(50+Δf sqi)]；
    当f i,n+1<50-Δf sqi时，T i,n+1＝T i,n+K Ti×[(50-Δf sqi)-f i,n+1]；
    当f i,n+1≥50-Δf sqi且f i,n+1≤50+Δf sqi时，T i,n+1＝T i,n；
    其中，K Ti是调频系数，Δf sqi是死区频率。
  7. 根据权利要求2所述的基于直算法的电力系统机电暂态仿真方法，其特征在于，所述步骤D中进行励磁调节时，发电机的励磁调节只能在不调节、电压调节、无功调节和功率因数调节这四种之中选择一种：
    若发电机不参与励磁调节，则I Li,n+1＝I Li,n；
    若是电压调节发电机，则有：
    当U i,n>U sdi+ΔU sqi时，I Li,n+1＝I Li,n-K ui×[U i,n-(U sdi+ΔU sqi)]；
    当U i,n<U sdi-ΔU sqi时，I Li,n+1＝I Li,n+K ui×[(U sdi-ΔU sqi)-U i,n]；
    当U i,n≥U sdi-ΔU sqi且U i,n≤U sdi+ΔU sqi时，I Li,n+1＝I Li,n；
    若是无功调节发电机，则有：
    当Q i,n>Q sdi+ΔQ sqi时，I Li,n+1＝I Li,n-K Qi×[Q i,n-(Q sdi+ΔQ sqi)]；
    当Q i,n<Q sdi-ΔQ sqi时，I Li,n+1＝I Li,n+K Qi×[(Q sdi-ΔQ sqi)-Q i,n]；
    当Q i,n≥Q sdi-ΔQ sqi且Q i,n≤Q sdi+ΔQ sqi时，I Li,n+1＝I Li,n；
    若是功率因数调节发电机，则有：
    当COS i,n>COS sdi+ΔCOS sqi时，I Li,n+1＝I Li,n+K COSi×[COS i,n-(COS sdi+ΔCOS sqi)]；
    当COS i,n<COS sdi-ΔCOS sqi时，I Li,n+1＝I Li,n-K COSi×[(COS sdi-ΔCOS sqi)-COS i,n]；
    当COS i,n≥COS sdi-ΔCOS sqi且COS i,n≤COS sdi+ΔCOS sqi时，I Li,n+1＝I Li,n；
    其中，K ui是发电机的电压调节系数，U sdi是设定电压，ΔU sqi是死区电压，U i,n 是第i节点发电机第n帧端口电压，K Qi是发电机的无功调节系数，Q sdi是设定无功功率，ΔQ sqi是死区无功功率，Q i,n是第i节点发电机第n帧输出无功功率，K COSi是发电机的功率因数调节系数，COS sdi是设定功率因数，ΔCOS sqi是死区功率因数，COS i,n是第i节点发电机第n帧功率因数。
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