CN114912300A - Rapid time domain simulation method for electric power system - Google Patents

Rapid time domain simulation method for electric power system Download PDF

Info

Publication number
CN114912300A
CN114912300A CN202210829815.5A CN202210829815A CN114912300A CN 114912300 A CN114912300 A CN 114912300A CN 202210829815 A CN202210829815 A CN 202210829815A CN 114912300 A CN114912300 A CN 114912300A
Authority
CN
China
Prior art keywords
power
generator
order
differential
state variable
Prior art date
Legal status (The legal status 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 status listed.)
Granted
Application number
CN202210829815.5A
Other languages
Chinese (zh)
Other versions
CN114912300B (en
Inventor
赵红生
任羽纶
王博
徐秋实
徐慎凯
刘承锡
余轶
王俊琪
熊志
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Wuhan University WHU
Economic and Technological Research Institute of State Grid Hubei Electric Power Co Ltd
Original Assignee
Wuhan University WHU
Economic and Technological Research Institute of State Grid Hubei Electric Power Co Ltd
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 Wuhan University WHU, Economic and Technological Research Institute of State Grid Hubei Electric Power Co Ltd filed Critical Wuhan University WHU
Priority to CN202210829815.5A priority Critical patent/CN114912300B/en
Publication of CN114912300A publication Critical patent/CN114912300A/en
Application granted granted Critical
Publication of CN114912300B publication Critical patent/CN114912300B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/04—Power grid distribution 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
    • H02J2203/20—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

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Theoretical Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • General Engineering & Computer Science (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • Operations Research (AREA)
  • Power Engineering (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • Computing Systems (AREA)
  • Supply And Distribution Of Alternating Current (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

A quick time domain simulation method of an electric power system comprises the steps of firstly carrying out differential transformation on a dynamic differential equation and an algebraic equation of the electric power system to obtain a corresponding differential transformation formula, then carrying out cross calculation by using the dynamic differential equation and the differential transformation formula of the algebraic equation based on initial values of state variables and node voltages of the electric power system to determine analytical solutions of the state variables and the node voltages at the time point, then calculating the state variables and the node voltage values at the next time point by using an inverse transformation formula of the differential transformation and a set time step, carrying out cross calculation again by using the state variables and the node voltage values as initial values of power series coefficients to obtain the analytical solutions of the state variables and the node voltages at the next time point, continuously circulating until a simulation duration is reached, obtaining the state variables and the node voltage values at the time points at this time, and finishing time domain simulation. The invention obviously improves the calculation speed and is beneficial to the dynamic analysis and control of the power system.

Description

Rapid time domain simulation method for electric power system
Technical Field
The invention belongs to the technical field of power system simulation, and particularly relates to a rapid time domain simulation method for a power system.
Background
In recent years, with the rapid development of social economy, the demand for electric energy is rapidly increased, and the operation of a power grid is gradually close to a saturation state. However, the infrastructure speed of the power system is more difficult to match with the increasing power demand, so that the power system gradually approaches its stability limit. Meanwhile, with the grid connection of wind power generation and solar power generation, the randomness and the volatility of new energy greatly influence the dynamic performance of a power system, and a brand new challenge is brought to the dynamic security assessment of the system. Accelerating the dynamic simulation of the power system has been a hot point of research.
The power system is a nonlinear high-order dynamic system, and for dynamic time domain simulation of the power system, a common method is to solve a differential algebraic equation system of the system to obtain the change conditions of state variables and non-state variables of the system, so as to obtain the change of the two variables along with time. The differential equation is solved in a numerical integration mode, the algebraic equation belongs to a nonlinear equation, and the algebraic equation is solved in an iteration mode. In order to meet the requirements of calculation accuracy and calculation result convergence, the step length of numerical integration cannot be selected to be too long, and after the state variable at the next time point is obtained, the value of the non-state variable needs to be updated through multiple iterative calculations, so that the calculated amount is very large, and the calculation time length increases nonlinearly with the increase of the network scale. In addition, when the system network equation is too complex, the computation speed may be further reduced or even unable to converge. Xiao Lei, Qiu Yi Ph, Wu Hao. The uncertainty analysis (power system automation, 2017, 41 (6): 59-65) "of the power system time domain simulation based on the generalized polynomial chaos method adds uncertainty into the time domain simulation, but the network equation is too complex, so that the application of the network equation in a large system is difficult.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provide a quick time domain simulation method for an electric power system, which can obviously improve the calculation speed.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
a quick time domain simulation method of a power system sequentially comprises the following steps:
a, carrying out differential transformation on a dynamic differential equation and an algebraic equation of the power system to obtain a corresponding differential transformation formula;
b, performing cross calculation by using a differential transformation formula of a dynamic differential equation and an algebraic equation based on the initial values of the state variables and the node voltage of the power system to determine the analytic solutions of the state variables and the node voltage at the time point;
step C, firstly adopting an inverse transformation formula of differential transformation and a set time step to calculate each state variable and node voltage value at the next time point, and then repeating the step B to obtain an analytic solution of each state variable and node voltage at the next time point;
and D, circularly repeating the step C until the simulation time length is reached, finally obtaining each state variable and node voltage value at each time point, and finishing time domain simulation at the moment.
In step a, the dynamic differential equation is:
Figure 244518DEST_PATH_IMAGE001
Figure 630500DEST_PATH_IMAGE002
in the above formula, the state variable
Figure 3713DEST_PATH_IMAGE003
、
Figure 867764DEST_PATH_IMAGE004
、
Figure 524879DEST_PATH_IMAGE005
、
Figure 612921DEST_PATH_IMAGE006
、
Figure 348795DEST_PATH_IMAGE007
、
Figure 875592DEST_PATH_IMAGE008
Are respectively the firstiRotor angle, rotational speed difference of the platform generator,qAxial transient potential,dAxial transient potential,qAxial sub-transient potentials anddaxial sub-transient potential, state variable
Figure 13312DEST_PATH_IMAGE009
Is as followsiExciting voltage, state variable of exciter corresponding to platform generator
Figure 350884DEST_PATH_IMAGE010
Is as followsiThe points above each state variable represent the integration of the mechanical power input by the speed regulator corresponding to the platform generator,Gin order to be able to count the number of generators,
Figure 574055DEST_PATH_IMAGE011
is the standard frequency of 50Hz,
Figure 576646DEST_PATH_IMAGE012
is as followsiThe electrical power of the station generator is,
Figure 693506DEST_PATH_IMAGE013
、
Figure 326613DEST_PATH_IMAGE014
are respectively the firstiThe damping constant and the inertia constant of the platform generator,
Figure 402192DEST_PATH_IMAGE015
、
Figure 942895DEST_PATH_IMAGE016
、
Figure 55207DEST_PATH_IMAGE017
are respectively the firstiTable generatordSynchronous reactance, transient reactance, sub-transient reactance of the axis,
Figure 718270DEST_PATH_IMAGE018
、
Figure 916033DEST_PATH_IMAGE019
are respectively the firstiTable generatordThe open-loop transient time constant and the sub-transient time constant of the shaft,
Figure 260427DEST_PATH_IMAGE020
、
Figure 102612DEST_PATH_IMAGE021
、
Figure 77521DEST_PATH_IMAGE022
are respectively the firstiTable generatorqSynchronous reactance, transient reactance, sub-transient reactance of the axis,
Figure 621635DEST_PATH_IMAGE023
、
Figure 769720DEST_PATH_IMAGE024
are respectively the firstiTable generatorqThe open-loop transient time constant and the sub-transient time constant of the shaft,
Figure 591045DEST_PATH_IMAGE025
、
Figure 376336DEST_PATH_IMAGE026
are respectively the firstiTable generatordA shaft,qThe current of the stator of the shaft is,
Figure 17533DEST_PATH_IMAGE027
is as followsiThe constant of the corresponding exciter of the counter generator,
Figure 31626DEST_PATH_IMAGE028
、
Figure 973037DEST_PATH_IMAGE029
、
Figure 352065DEST_PATH_IMAGE030
are respectively the firstiConstant reference voltage, node voltage amplitude and electromagnetic torque of an exciter corresponding to the platform generator,
Figure 621504DEST_PATH_IMAGE031
、
Figure 49074DEST_PATH_IMAGE032
are respectively the firstiConstant reference power and mechanical torque of a speed regulator corresponding to the platform generator,
Figure 704046DEST_PATH_IMAGE033
is as followsiThe constant of the speed regulator corresponding to the platform generator,
Figure 253976DEST_PATH_IMAGE034
、
Figure 135345DEST_PATH_IMAGE035
are respectively the firstiStator of platform generatordA shaft,qThe terminal voltage of the shaft is measured,y、rfor the purpose of transforming the matrix for the coordinate system,
Figure 9016DEST_PATH_IMAGE036
is as followsiThe internal resistance of the station generator is increased,
Figure 393861DEST_PATH_IMAGE037
、
Figure 177009DEST_PATH_IMAGE038
are respectively the firstiTable generatorxA shaft,yThe current of the stator of the shaft is,
Figure 342412DEST_PATH_IMAGE039
、
Figure 377364DEST_PATH_IMAGE040
are respectively the firstiStator of platform generatorxA shaft,yShaft end voltage;
the differential transformation formula corresponding to the dynamic differential equation is as follows:
Figure 757661DEST_PATH_IMAGE041
in the above formula, the first and second carbon atoms are,
Figure 383814DEST_PATH_IMAGE042
、
Figure 239775DEST_PATH_IMAGE043
、
Figure 203051DEST_PATH_IMAGE044
、
Figure 296909DEST_PATH_IMAGE045
、
Figure 936707DEST_PATH_IMAGE046
、
Figure 811122DEST_PATH_IMAGE047
、
Figure 453456DEST_PATH_IMAGE048
、
Figure 792033DEST_PATH_IMAGE049
are respectively as
Figure 228831DEST_PATH_IMAGE050
、
Figure 669171DEST_PATH_IMAGE004
、
Figure 646354DEST_PATH_IMAGE051
、
Figure 980383DEST_PATH_IMAGE006
、
Figure 447137DEST_PATH_IMAGE052
、
Figure 499406DEST_PATH_IMAGE008
、
Figure 14701DEST_PATH_IMAGE009
、
Figure 845648DEST_PATH_IMAGE053
To (1) akThe coefficient of the power series of the +1 order,
Figure 624248DEST_PATH_IMAGE054
、
Figure 22868DEST_PATH_IMAGE055
、
Figure 341854DEST_PATH_IMAGE056
、
Figure 650475DEST_PATH_IMAGE057
、
Figure 209764DEST_PATH_IMAGE058
、
Figure 971047DEST_PATH_IMAGE059
are respectively as
Figure 421619DEST_PATH_IMAGE004
、
Figure 381485DEST_PATH_IMAGE060
、
Figure 501888DEST_PATH_IMAGE061
、
Figure 124368DEST_PATH_IMAGE051
、
Figure 988419DEST_PATH_IMAGE052
、
Figure 802791DEST_PATH_IMAGE062
To (1) akThe coefficient of the power series of the order,
Figure 484308DEST_PATH_IMAGE063
、
Figure 220183DEST_PATH_IMAGE064
、
Figure 763291DEST_PATH_IMAGE065
、
Figure 369853DEST_PATH_IMAGE066
、
Figure 894375DEST_PATH_IMAGE067
are respectively as
Figure 242180DEST_PATH_IMAGE006
、
Figure 182454DEST_PATH_IMAGE008
、
Figure 551512DEST_PATH_IMAGE025
、
Figure 450198DEST_PATH_IMAGE026
、
Figure 691823DEST_PATH_IMAGE029
To (1) akThe coefficient of the power series of the order,
Figure 826001DEST_PATH_IMAGE068
is a function of kronecker, if and only ifkThe function output is 1 when =0, and the output is 0 in other cases.
In step a, the algebraic equation is:
Figure 672734DEST_PATH_IMAGE069
Figure 352109DEST_PATH_IMAGE070
Figure 346609DEST_PATH_IMAGE071
in the above formula, the first and second carbon atoms are,
Figure 894265DEST_PATH_IMAGE072
in order to be a system admittance matrix,
Figure 720139DEST_PATH_IMAGE073
is the voltage of the node, and is,
Figure 695048DEST_PATH_IMAGE074
in order to be the node current,
Figure 176845DEST_PATH_IMAGE075
is shaped likeThe state variable is changed into the variable,
Figure 902093DEST_PATH_IMAGE076
、
Figure 723419DEST_PATH_IMAGE077
transforming matrices to coordinate systemsyAndrthe parameters that are relevant are set to the parameters,g、l、z、i、prespectively a generator, a load, a pure impedance load, a pure current load and a pure power load,
Figure 993863DEST_PATH_IMAGE078
、
Figure 900639DEST_PATH_IMAGE079
、
Figure 586836DEST_PATH_IMAGE080
respectively are the occupation ratio matrixes of pure impedance load, pure current load and pure power load,
Figure 403613DEST_PATH_IMAGE081
is as followsiThe bus voltage when the platform generator is in a steady state,
Figure 454746DEST_PATH_IMAGE082
which is the square of the voltage at the node,
Figure 973452DEST_PATH_IMAGE083
、
Figure 463339DEST_PATH_IMAGE084
respectively active power and reactive power in a steady state,
Figure 851069DEST_PATH_IMAGE085
、
Figure 400999DEST_PATH_IMAGE086
respectively the proportion of pure impedance load in active power and reactive power,
Figure 282367DEST_PATH_IMAGE087
、
Figure 372683DEST_PATH_IMAGE088
the proportion of pure current load in active power and reactive power respectively,
Figure 23107DEST_PATH_IMAGE089
、
Figure 743938DEST_PATH_IMAGE090
are the ratio of pure power load in active power and reactive power respectively, and
Figure 987969DEST_PATH_IMAGE091
、
Figure 757342DEST_PATH_IMAGE092
；
the differential transformation of the algebraic equation is:
Figure 386906DEST_PATH_IMAGE093
Figure 481901DEST_PATH_IMAGE094
in the above formula, the first and second carbon atoms are,
Figure 134600DEST_PATH_IMAGE095
、
Figure 81565DEST_PATH_IMAGE096
、
Figure 441002DEST_PATH_IMAGE097
、
Figure 831532DEST_PATH_IMAGE098
、
Figure 705947DEST_PATH_IMAGE099
are respectively as
Figure 348281DEST_PATH_IMAGE100
、
Figure 437591DEST_PATH_IMAGE101
、
Figure 874388DEST_PATH_IMAGE102
、
Figure 236100DEST_PATH_IMAGE103
、
Figure 275600DEST_PATH_IMAGE104
To (1) akThe coefficient of the power series of the order,A、Bin the form of a matrix of coefficients,
Figure 609629DEST_PATH_IMAGE105
、
Figure 594159DEST_PATH_IMAGE106
is a matrix of coefficients of the generator,
Figure 646429DEST_PATH_IMAGE107
、
Figure 161724DEST_PATH_IMAGE108
is a coefficient matrix of the load, an
Figure 740472DEST_PATH_IMAGE105
、
Figure 253493DEST_PATH_IMAGE106
、
Figure 668425DEST_PATH_IMAGE109
、
Figure 987411DEST_PATH_IMAGE108
Including the front of the state variablekFront of order power series coefficient and non-algebraic variablek-power series coefficients of order 1.
The step B comprises the following steps in sequence:
step B1, inputting the initial values of the state variables and the node voltage of the power systemx 0 Andv 0 is that isX[0]、V[0]Then, the 1 st order power series coefficient of each state variable is calculated based on the differential transformation formula of the dynamic differential equation and the differential transformation formula of the algebraic equationX[1]1 st order power series coefficient of node voltageV[1]；
Step B2, repeating step B1 circularly until the orderkAnd when the maximum value is reached, obtaining each state variable and node voltage value at the time point.
Compared with the prior art, the invention has the beneficial effects that:
the invention relates to a rapid time domain simulation method of an electric power system, which firstly carries out differential transformation on a dynamic differential equation and an algebraic equation of the electric power system to obtain a corresponding differential transformation formula, then carries out cross calculation by utilizing the differential transformation formula of the dynamic differential equation and the algebraic equation based on initial values of state variables and node voltages of the electric power system to determine analytical solutions of the state variables and the node voltages at the time point, then calculates the state variables and the node voltage values at the next time point by adopting an inverse transformation formula of the differential transformation and a set time step, carries out cross calculation again by taking the state variables and the node voltage values as initial values of power series coefficients to obtain the analytical solutions of the state variables and the node voltages at the next time point, continuously circulates until a simulation duration is reached, finally obtains the state variables and the node voltage values at the time points, and on one hand, changes an iterative process into a recursion process through the differential transformation method, the nonlinear variables are expressed as a linear relation, so that the step length of time domain simulation can be obviously increased, the calculated amount is greatly reduced, the calculating speed is improved, the emergency can be analyzed and early warned more quickly, and on the other hand, the variables are decoupled through differential transformation, and the analysis and control of the variables are facilitated. Therefore, the method and the device remarkably improve the calculation speed and are beneficial to dynamic analysis and control of the power system.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a topology diagram of an IEEE 39 node system employed in embodiment 1.
Fig. 3 is a schematic diagram of the crossover calculation process in example 1.
FIG. 4 shows the calculation results of the time step of 0.01s in example 1.
FIG. 5 shows the calculation results of the time step of 0.02s in example 1.
FIG. 6 is a graph comparing the method of the present invention with a conventional method.
Fig. 7 shows the influence of the maximums of different orders on the calculation error and time length.
Detailed Description
The present invention will be described in further detail with reference to the following detailed description and accompanying drawings.
The invention provides a power system rapid time domain simulation technology based on differential transformation, which establishes a differential transformation formula of a differential algebraic equation set of a power system through a differential transformation method, and then obtains power series coefficients of all variables through alternative calculation of the differential transformation formula of the differential equation and the differential transformation formula of the algebraic equation to obtain an analytic solution of the variables, thereby solving the problem of nonlinear coupling among all the variables and realizing rapid time domain simulation of the power system. The technology can convert nonlinear algebraic equations into linear equations by applying a differential transformation method without carrying out a large amount of iterative calculations, can obtain the analytic solution of each variable, and can greatly increase the calculation time step when the calculation order is high enough, thereby reducing the calculation amount again and greatly reducing the simulation time length. Simulation results show that the technology can remarkably improve the time domain simulation speed of a large-scale power system under the condition of meeting the requirement of precision, and provides a new idea for dynamic analysis of the power system.
In the present invention, the differential transformation method is defined as follows:
to one or moretAs a function of the argumentx(t) A positive transformation expression whose differential transformation can be defined as:
Figure 296033DEST_PATH_IMAGE110
it can be seen that the positive transformation of the differential transformation is a pair functionx(t) In thatt i Processing and calculatingkThe second derivative. At the same time, when the functionx(t) In Taylor expansion oft i When converging in the neighborhood, the inverse of the differential transform can be written as:
Figure 104589DEST_PATH_IMAGE111
the formula from which the inverse transformation can be derived is in fact a functionx(t) In thatt i Taylor expansion of (1), in whichX[k]Representing different order power series coefficients.
Introducing the concept of differential transformation into power systemt i =0, while the differential transformation definition is modified appropriately, the expression of the modified differential transformation positive and negative transformation is as follows:
Figure 865871DEST_PATH_IMAGE112
at this time, the differential conversionX[k]Representing variablesx(t) In thattThe power series coefficient of the taylor expansion at time point = 0.
Example 1:
referring to fig. 1, a method for fast time domain simulation of an electric power system, which takes an IEEE 39 node system (which is a new england system with 10 motors and 39 nodes, 10 conventional thermal power plants, dynamic components including a generator, an exciter and a speed regulator, and loads being ZIP loads, wherein a pure resistance load accounts for 20%, a pure current load accounts for 30%, and a pure power load accounts for 50%) shown in fig. 2 as a research object, and simulates a short-circuit fault of a period duration occurring in the system at the 1 st s, the method of the present invention simulates a state variable of the system and a change condition of a node voltage within 10s after the fault is removed, and sequentially includes the following steps:
1. carrying out differential transformation on a dynamic differential equation and an algebraic equation of the power system to obtain a corresponding differential transformation formula, wherein the differential transformation of the dynamic differential equation is as follows:
in the dynamic simulation of the power system, the state variables of various dynamic devices (such as a generator, an exciter and the like) in the system are expressed by differential equations, the differential equations are solved by numerical integration, and a 6-order synchronous generator model, a 1-order exciter model and a 1-order governor model are considered, and the system dynamic differential equations are as follows:
Figure 988548DEST_PATH_IMAGE113
Figure 525578DEST_PATH_IMAGE114
in the above formula, the state variable
Figure 645980DEST_PATH_IMAGE115
、
Figure 284772DEST_PATH_IMAGE116
、
Figure 883244DEST_PATH_IMAGE117
、
Figure 776245DEST_PATH_IMAGE118
、
Figure 333128DEST_PATH_IMAGE119
、
Figure 865740DEST_PATH_IMAGE120
Are respectively the firstiRotor angle, rotation speed difference of platform generator,qAxial transient potential,dAxial transient potential,qAxial sub-transient potentials anddaxial sub-transient potential, state variable
Figure 392537DEST_PATH_IMAGE121
Is as followsiExciting voltage, state variable of exciter corresponding to platform generator
Figure 530257DEST_PATH_IMAGE122
Is a firstiThe points above each state variable represent the integration of the mechanical power input by the speed regulator corresponding to the platform generator,Gin order to be able to count the number of generators,
Figure 634873DEST_PATH_IMAGE123
is the standard frequency of 50Hz,
Figure 592464DEST_PATH_IMAGE124
is as followsiThe electrical power of the station generator is,
Figure 922951DEST_PATH_IMAGE125
、
Figure 728228DEST_PATH_IMAGE126
are respectively the firstiThe damping constant and the inertia constant of the platform generator,
Figure 220389DEST_PATH_IMAGE127
、
Figure 304757DEST_PATH_IMAGE128
、
Figure 314301DEST_PATH_IMAGE129
are respectively the firstiTable generatordSynchronous reactance, transient reactance, sub-transient reactance of the axis,
Figure 285669DEST_PATH_IMAGE130
、
Figure 89676DEST_PATH_IMAGE131
are respectively the firstiTable generatordThe open-loop transient time constant and the sub-transient time constant of the shaft,
Figure 897227DEST_PATH_IMAGE132
、
Figure 507200DEST_PATH_IMAGE133
、
Figure 474019DEST_PATH_IMAGE134
are respectively the firstiTable generatorqSynchronous reactance, transient reactance, sub-transient reactance of the axis,
Figure 307982DEST_PATH_IMAGE135
、
Figure 993042DEST_PATH_IMAGE136
are respectively the firstiTable generatorqThe open-loop transient time constant and the sub-transient time constant of the shaft,
Figure 141126DEST_PATH_IMAGE137
、
Figure 339283DEST_PATH_IMAGE138
are respectively the firstiTable generatordA shaft,qThe current of the stator of the shaft is,
Figure 485093DEST_PATH_IMAGE139
is as followsiThe constant of the corresponding exciter of the counter generator,
Figure 250924DEST_PATH_IMAGE140
、
Figure 405962DEST_PATH_IMAGE141
、
Figure 878531DEST_PATH_IMAGE142
are respectively the firstiConstant reference voltage, node voltage amplitude and electromagnetic torque of an exciter corresponding to the platform generator,
Figure 336189DEST_PATH_IMAGE143
、
Figure 730261DEST_PATH_IMAGE144
are respectively the firstiThe constant reference power and the mechanical torque of the speed regulator corresponding to the platform generator,
Figure 282465DEST_PATH_IMAGE145
is as followsiThe constant of the speed regulator corresponding to the platform generator,
Figure 78383DEST_PATH_IMAGE146
、
Figure 205476DEST_PATH_IMAGE147
are respectively the firstiStator of platform generatordA shaft,qThe terminal voltage of the shaft is measured,y、rfor the purpose of transforming the matrix for the coordinate system,
Figure 618003DEST_PATH_IMAGE148
is as followsiThe internal resistance of the station generator is increased,
Figure 114844DEST_PATH_IMAGE101
、
Figure 624322DEST_PATH_IMAGE102
are respectively the firstiTable generatorxA shaft,yThe current of the stator of the shaft is,
Figure 548416DEST_PATH_IMAGE149
、
Figure 713818DEST_PATH_IMAGE150
are respectively the firstiStator of platform generatorxA shaft,yThe shaft end voltage.
According to the definition of differential transformation, only the variable in the differential equation needs to be changed into the corresponding second variablekThe coefficients of the power series are represented by corresponding capital letters, and the other coefficients remain unchanged. The differential operation of the state variables is shown on the left of the motion equations of the generator, exciter and speed regulator, and becomesk+1) power series coefficient of the order, the other variables on the right side become the first ones after transformationkThe order coefficient, all constant parameters remain unchanged, and all coefficients of the power series are represented by corresponding capital letters, so that the differential transformation equation corresponding to the dynamic differential equation is:
Figure 624136DEST_PATH_IMAGE041
in the above formula, the first and second carbon atoms are,
Figure 863488DEST_PATH_IMAGE151
、
Figure 83117DEST_PATH_IMAGE152
、
Figure 673498DEST_PATH_IMAGE153
、
Figure 308879DEST_PATH_IMAGE154
、
Figure 299007DEST_PATH_IMAGE155
、
Figure 299324DEST_PATH_IMAGE156
、
Figure 501636DEST_PATH_IMAGE157
、
Figure 675128DEST_PATH_IMAGE158
are respectively as
Figure 154651DEST_PATH_IMAGE115
、
Figure 201235DEST_PATH_IMAGE116
、
Figure 766209DEST_PATH_IMAGE159
、
Figure 71288DEST_PATH_IMAGE118
、
Figure 467635DEST_PATH_IMAGE119
、
Figure 75333DEST_PATH_IMAGE120
、
Figure 970346DEST_PATH_IMAGE160
、
Figure 954483DEST_PATH_IMAGE161
To (1) akThe coefficient of the power series of the +1 order,
Figure 205335DEST_PATH_IMAGE162
、
Figure 108569DEST_PATH_IMAGE163
、
Figure 382556DEST_PATH_IMAGE164
、
Figure 514591DEST_PATH_IMAGE165
、
Figure 823213DEST_PATH_IMAGE166
、
Figure 569452DEST_PATH_IMAGE167
are respectively as
Figure 720947DEST_PATH_IMAGE116
、
Figure 515728DEST_PATH_IMAGE168
、
Figure 321266DEST_PATH_IMAGE169
、
Figure 441669DEST_PATH_IMAGE170
、
Figure 486986DEST_PATH_IMAGE119
、
Figure 210091DEST_PATH_IMAGE171
To (1) akThe coefficient of the power series of the order,
Figure 493305DEST_PATH_IMAGE172
、
Figure 581346DEST_PATH_IMAGE173
、
Figure 192587DEST_PATH_IMAGE174
、
Figure 860329DEST_PATH_IMAGE175
、
Figure 122683DEST_PATH_IMAGE176
are respectively as
Figure 319309DEST_PATH_IMAGE118
、
Figure 916382DEST_PATH_IMAGE120
、
Figure 184552DEST_PATH_IMAGE137
、
Figure 176779DEST_PATH_IMAGE138
、
Figure 668940DEST_PATH_IMAGE141
To (1) akThe coefficient of the power series of the order,
Figure 379407DEST_PATH_IMAGE177
is a function of kronecker, if and only ifkThe function output is 1 when =0, and the output is 0 in other cases.
As can be seen from the above equation, the differential transformation equation of the differential transformation is a recursive equation, the left side of the equation is the high-order power coefficient of the state variable, and the right side of the equation has only the low-order coefficient, so that the power coefficient of the state variable can be recursively calculated by the above equation.
The differential transformation of the algebraic equation is:
since the node voltage and current in the power system are nonlinear, they can only be expressed by nonlinear algebraic equations:
Figure 185689DEST_PATH_IMAGE178
in the above formula, the first and second carbon atoms are,
Figure 907788DEST_PATH_IMAGE179
in order to be a system admittance matrix,
Figure 711796DEST_PATH_IMAGE100
is the voltage of the node, and is,
Figure 768614DEST_PATH_IMAGE180
in order to be the node current,
Figure 581849DEST_PATH_IMAGE075
is a state variable.
Meanwhile, the current injection model of the generator and the ZIP load is as follows:
Figure 79827DEST_PATH_IMAGE070
Figure 697146DEST_PATH_IMAGE181
in the above formula, the first and second carbon atoms are,
Figure 851047DEST_PATH_IMAGE076
、
Figure 327028DEST_PATH_IMAGE077
transforming matrices to coordinate systemsyAndrthe parameters that are relevant are set to the parameters,g、l、z、i、prespectively a generator, a load, a pure impedance load, a pure current load and a pure power load,
Figure 945091DEST_PATH_IMAGE182
、
Figure 356481DEST_PATH_IMAGE079
、
Figure 873044DEST_PATH_IMAGE080
respectively are the occupation ratio matrixes of pure impedance load, pure current load and pure power load,
Figure 28082DEST_PATH_IMAGE081
is as followsiThe bus voltage when the platform generator is in a steady state,
Figure 500651DEST_PATH_IMAGE082
which is the square of the voltage at the node,
Figure 207576DEST_PATH_IMAGE183
、
Figure 336069DEST_PATH_IMAGE084
respectively active power and reactive power in a steady state,
Figure 403120DEST_PATH_IMAGE085
、
Figure 995775DEST_PATH_IMAGE184
respectively the proportion of pure impedance load in active power and reactive power,
Figure 483389DEST_PATH_IMAGE087
、
Figure 223811DEST_PATH_IMAGE088
the proportion of pure current load in active power and reactive power respectively,
Figure 720652DEST_PATH_IMAGE089
、
Figure 246442DEST_PATH_IMAGE185
are the ratio of pure power load in active power and reactive power respectively, and
Figure 967274DEST_PATH_IMAGE091
、
Figure 70359DEST_PATH_IMAGE092
；
according to the basic definition of differential transformation, the current injection equations of the motor and the load are transformed, and power series coefficients of the current injected by the generator and the ZIP load are written into the same form through a series of mathematical deductions:
Figure 964365DEST_PATH_IMAGE186
in the above formula, the first and second carbon atoms are,
Figure 846127DEST_PATH_IMAGE187
、
Figure 675543DEST_PATH_IMAGE097
、
Figure 390558DEST_PATH_IMAGE188
、
Figure 25939DEST_PATH_IMAGE189
are respectively as
Figure 650955DEST_PATH_IMAGE190
、
Figure 792218DEST_PATH_IMAGE102
、
Figure 604316DEST_PATH_IMAGE103
、
Figure 105704DEST_PATH_IMAGE191
To (1)kThe coefficient of the power series of the order,
Figure 381965DEST_PATH_IMAGE105
、
Figure 818762DEST_PATH_IMAGE192
is a matrix of coefficients of the generator,
Figure 492058DEST_PATH_IMAGE193
、
Figure 672504DEST_PATH_IMAGE194
is a coefficient matrix of the load, an
Figure 803271DEST_PATH_IMAGE105
、
Figure 535603DEST_PATH_IMAGE192
、
Figure 587873DEST_PATH_IMAGE195
、
Figure 181797DEST_PATH_IMAGE194
Containing only state variableskFront of order power series coefficient and non-algebraic variablekPower series coefficients of order 1, so the two equations are explicit linear equations.
Since the injection current of the generator and the injection current of the ZIP load are opposite in direction, the two equations are subtracted to obtain a differential transformation equation of the node equivalent injection current equation:
Figure 370332DEST_PATH_IMAGE196
in the above formula, the first and second carbon atoms are,
Figure 945670DEST_PATH_IMAGE197
、
Figure 609870DEST_PATH_IMAGE198
respectively, differential transformation of node current and voltage,
Figure 866539DEST_PATH_IMAGE197
Included
Figure 563710DEST_PATH_IMAGE199
and
Figure 513212DEST_PATH_IMAGE200
，
Figure 336811DEST_PATH_IMAGE198
Included
Figure 521805DEST_PATH_IMAGE201
and
Figure 419354DEST_PATH_IMAGE202
and is and
Figure 680702DEST_PATH_IMAGE203
left side of the above formula is the first of node currentkCoefficient of power series of order, right side containing only voltagekThe power series coefficients of the order and the coefficients of the lower order of the other variables, i.e. the current and voltage of the system are represented by linear equations by differential transformation. Substituting the above formula into a nonlinear algebraic equation of the system to obtain a recursion formula for calculating the voltage power series coefficient:
Figure 726018DEST_PATH_IMAGE093
according to the above formula and the differential transformation formula of the node current, the high-order power series coefficient of the voltage and the current can be calculated through the low-order power series coefficient, and the iterative process is changed into a recursion process.
2. Firstly inputting initial values of each state variable and node voltage of the power systemx 0 Andv 0 is that isX[0]、V[0]Based on the differential transformation formula corresponding to the dynamic differential equation, the 1 st order power series coefficient of each state variable is calculatedX[1]Then, a coefficient matrix is calculated based on a differential transformation formula of an algebraic equationAAndB1 st order power series coefficient of node voltageV[1]1 st order power series coefficient of node currentI[1]The coefficients of the state variables and the 1 st power series of the node voltage are obtainedX[1]AndV[1]；
3. according to state variable and node electricityCoefficient of the 1 st order power seriesX[1]AndV[1]calculating the 2 nd order power series coefficient of each state variable based on the differential transformation formula corresponding to the dynamic differential equationX[2]Then, a coefficient matrix is calculated based on a differential transformation formula of an algebraic equationAAndB2 nd order power series coefficient of node voltageV[2]2 nd order power series coefficient of node currentI[2]At this time, the state variable and the coefficient of the 2 nd power series of the node voltage are obtainedX[2]AndV[2]；
4. repeating the step 3 circularly until the orderkWhen the maximum value reaches 3, the analytical values of the state variables and the node voltages at the time point are obtained, and the whole cross calculation process is shown in fig. 3;
5. firstly, adopting inverse transformation formula of differential transformation and set time step length of 0.01s to calculate various state variables and node voltage values of next time point, then using them as initial valuesx 0 Andv 0 sequentially repeating the steps 2, 3 and 4 to obtain the analytical values of the state variables and the node voltage at the next time point;
6. and (5) circularly repeating the step until the simulation time is reached, obtaining each state variable and node voltage value at each time point, and completing time domain simulation, wherein the simulation result is shown in FIG. 4.
To investigate the effectiveness of the method of the invention, the following tests were carried out:
the time step is set to 0.02s, and time domain simulation is performed according to the method described in embodiment 1, and the result is shown in fig. 5. As can be seen by comparing FIG. 4 and FIG. 5, the time-domain error of the generator rotor angle is more obvious when the time step is selected to be 0.02s, but the calculation result can still maintain the convergence and stability.
Comparing the simulation result of the embodiment 1 with the time domain simulation result of the IEEE 39 node system using the traditional antecedent eulerian method, the result is shown in fig. 6 (where the dotted line is the simulation result of the antecedent eulerian method, and the calculation step size is 0.001 s).
FIG. 6 shows that the time-domain error of the generator rotor angle is smaller than the Euler method.
FIG. 7 shows the calculation time length and the calculation time length of the order maximum K to the simulation calculationAs can be seen from the influence of the calculation error, as the K value is increased from 2 to 3, the calculation accuracy of the state variable and the node voltage is improved, and at the moment, the voltage error and the rotation speed error are both in an acceptable range, but the increase of the K value can not obviously improve the calculation accuracy, but can increase the calculation load and increase the calculation time, so that the method selects K=3, the accuracy requirement can be met, the calculation amount is reduced, and the calculation time is shortened.

Claims (4)

1. A quick time domain simulation method of an electric power system is characterized in that:
the method comprises the following steps in sequence:
step A, carrying out differential transformation on a dynamic differential equation and an algebraic equation of the power system to obtain a corresponding differential transformation formula;
b, performing cross calculation by using a differential transformation formula of a dynamic differential equation and an algebraic equation based on the initial values of the state variables and the node voltage of the power system to determine the analytic solutions of the state variables and the node voltage at the time point;
step C, firstly adopting an inverse transformation formula of differential transformation and a set time step to calculate each state variable and node voltage value at the next time point, and then repeating the step B to obtain an analytic solution of each state variable and node voltage at the next time point;
and D, circularly repeating the step C until the simulation time length is reached, finally obtaining each state variable and node voltage value at each time point, and finishing time domain simulation at the moment.
2. The method for rapid time domain simulation of an electric power system according to claim 1, wherein:
in step a, the dynamic differential equation is:
Figure 478695DEST_PATH_IMAGE001
Figure 192573DEST_PATH_IMAGE002
in the above formula, the state variable
Figure 552404DEST_PATH_IMAGE003
、
Figure 541088DEST_PATH_IMAGE004
、
Figure 824302DEST_PATH_IMAGE005
、
Figure 990972DEST_PATH_IMAGE006
、
Figure 992426DEST_PATH_IMAGE007
、
Figure 660168DEST_PATH_IMAGE008
Are respectively the firstiRotor angle, rotation speed difference of platform generator,qAxial transient potential,dAxial transient potential,qAxial sub-transient potentials anddaxial sub-transient potential, state variable
Figure 922522DEST_PATH_IMAGE009
Is as followsiExciting voltage, state variable of exciter corresponding to platform generator
Figure 650307DEST_PATH_IMAGE010
Is as followsiThe points above each state variable represent the integration of the mechanical power input by the speed regulator corresponding to the platform generator,Gin order to be able to count the number of generators,
Figure 247379DEST_PATH_IMAGE011
is the standard frequency of 50Hz,
Figure 718812DEST_PATH_IMAGE012
is as followsiTable generatorThe electric power of (a) is,
Figure 711039DEST_PATH_IMAGE013
、
Figure 999937DEST_PATH_IMAGE014
are respectively the firstiThe damping constant and the inertia constant of the platform generator,
Figure 710404DEST_PATH_IMAGE015
、
Figure 329736DEST_PATH_IMAGE016
、
Figure 707627DEST_PATH_IMAGE017
are respectively the firstiTable generatordSynchronous reactance, transient reactance, sub-transient reactance of the axis,
Figure 511635DEST_PATH_IMAGE018
、
Figure 99612DEST_PATH_IMAGE019
are respectively the firstiTable generatordThe open-loop transient time constant and the sub-transient time constant of the shaft,
Figure 647268DEST_PATH_IMAGE020
、
Figure 879666DEST_PATH_IMAGE021
、
Figure 508704DEST_PATH_IMAGE022
are respectively the firstiTable generatorqSynchronous reactance, transient reactance, sub-transient reactance of the axis,
Figure 193763DEST_PATH_IMAGE023
、
Figure 669744DEST_PATH_IMAGE024
are respectively the firstiTable generatorqThe open-loop transient time constant and the sub-transient time constant of the shaft,
Figure 756649DEST_PATH_IMAGE025
、
Figure 168038DEST_PATH_IMAGE026
are respectively the firstiTable generatordA shaft,qThe current of the stator of the shaft is,
Figure 215760DEST_PATH_IMAGE027
is as followsiThe constant of the corresponding exciter of the counter generator,
Figure 105219DEST_PATH_IMAGE028
、
Figure 312209DEST_PATH_IMAGE029
、
Figure 19134DEST_PATH_IMAGE030
are respectively the firstiConstant reference voltage, node voltage amplitude and electromagnetic torque of an exciter corresponding to the platform generator,
Figure 678785DEST_PATH_IMAGE031
、
Figure 745836DEST_PATH_IMAGE032
are respectively the firstiConstant reference power and mechanical torque of a speed regulator corresponding to the platform generator,
Figure 541754DEST_PATH_IMAGE033
is as followsiThe constant of the speed regulator corresponding to the platform generator,
Figure 294946DEST_PATH_IMAGE034
、
Figure 566528DEST_PATH_IMAGE035
are respectively the firstiStator of platform generatordA shaft,qThe terminal voltage of the shaft is measured,y、rfor the purpose of transforming the matrix for the coordinate system,
Figure 63368DEST_PATH_IMAGE036
is as followsiThe internal resistance of the station generator is increased,
Figure 589158DEST_PATH_IMAGE037
、
Figure 513252DEST_PATH_IMAGE038
are respectively the firstiTable generatorxA shaft,yThe current of the stator of the shaft is,
Figure 881917DEST_PATH_IMAGE039
、
Figure 307082DEST_PATH_IMAGE040
are respectively the firstiStator of platform generatorxA shaft,yShaft end voltage;
the differential transformation formula corresponding to the dynamic differential equation is as follows:
Figure 77592DEST_PATH_IMAGE041
in the above formula, the first and second carbon atoms are,
Figure 172587DEST_PATH_IMAGE042
、
Figure 405378DEST_PATH_IMAGE043
、
Figure 509600DEST_PATH_IMAGE044
、
Figure 993671DEST_PATH_IMAGE045
、
Figure 525147DEST_PATH_IMAGE046
、
Figure 602824DEST_PATH_IMAGE047
、
Figure 386104DEST_PATH_IMAGE048
、
Figure 865627DEST_PATH_IMAGE049
are respectively as
Figure 568003DEST_PATH_IMAGE050
、
Figure 257611DEST_PATH_IMAGE004
、
Figure 703635DEST_PATH_IMAGE051
、
Figure 411566DEST_PATH_IMAGE006
、
Figure 284844DEST_PATH_IMAGE052
、
Figure 337114DEST_PATH_IMAGE008
、
Figure 445884DEST_PATH_IMAGE009
、
Figure 899999DEST_PATH_IMAGE053
To (1) akThe coefficient of the power series of the +1 order,
Figure 553966DEST_PATH_IMAGE054
、
Figure 359111DEST_PATH_IMAGE055
、
Figure 881359DEST_PATH_IMAGE056
、
Figure 580193DEST_PATH_IMAGE057
、
Figure 529695DEST_PATH_IMAGE058
、
Figure 556557DEST_PATH_IMAGE059
are respectively as
Figure 259327DEST_PATH_IMAGE004
、
Figure 688034DEST_PATH_IMAGE060
、
Figure 933071DEST_PATH_IMAGE061
、
Figure 712808DEST_PATH_IMAGE062
、
Figure 576859DEST_PATH_IMAGE007
、
Figure 735439DEST_PATH_IMAGE063
To (1)kThe coefficient of the power series of the order,
Figure 292322DEST_PATH_IMAGE064
、
Figure 293776DEST_PATH_IMAGE065
、
Figure 86152DEST_PATH_IMAGE066
、
Figure 223872DEST_PATH_IMAGE067
、
Figure 325558DEST_PATH_IMAGE068
are respectively as
Figure 814308DEST_PATH_IMAGE006
、
Figure 20161DEST_PATH_IMAGE008
、
Figure 871443DEST_PATH_IMAGE025
、
Figure 35708DEST_PATH_IMAGE026
、
Figure 355962DEST_PATH_IMAGE029
To (1) akThe coefficient of the power series of the order,
Figure 631085DEST_PATH_IMAGE069
is a function of kronecker, if and only ifkThe function output is 1 when =0, and the output is 0 in other cases.
3. The method for rapid time domain simulation of an electric power system according to claim 2, wherein:
in step a, the algebraic equation is:
Figure 868032DEST_PATH_IMAGE070
Figure 937619DEST_PATH_IMAGE071
Figure 135382DEST_PATH_IMAGE072
in the above formula, the first and second carbon atoms are,
Figure 325448DEST_PATH_IMAGE073
in order to be a system admittance matrix,
Figure 292267DEST_PATH_IMAGE074
is the voltage of the node, and is,
Figure 391810DEST_PATH_IMAGE075
in order to be the node current,
Figure 811290DEST_PATH_IMAGE076
in order to be a state variable, the state variable,
Figure 38003DEST_PATH_IMAGE077
、
Figure 452804DEST_PATH_IMAGE078
converting a matrix to a coordinate systemyAndrthe parameters that are relevant are set to the parameters,g、l、z、i、prespectively a generator, a load, a pure impedance load, a pure current load and a pure power load,
Figure 129773DEST_PATH_IMAGE079
、
Figure 410451DEST_PATH_IMAGE080
、
Figure 565489DEST_PATH_IMAGE081
respectively are the occupation ratio matrixes of pure impedance load, pure current load and pure power load,
Figure 506900DEST_PATH_IMAGE082
is as followsiThe bus voltage when the platform generator is in a steady state,
Figure 948245DEST_PATH_IMAGE083
which is the square of the voltage at the node,
Figure 607897DEST_PATH_IMAGE084
、
Figure 176413DEST_PATH_IMAGE085
respectively active power and reactive power in a steady state,
Figure 706751DEST_PATH_IMAGE086
、
Figure 584577DEST_PATH_IMAGE087
respectively the proportion of pure impedance load in active power and reactive power,
Figure 731525DEST_PATH_IMAGE088
、
Figure 327898DEST_PATH_IMAGE089
the proportion of pure current load in active power and reactive power respectively,
Figure 978322DEST_PATH_IMAGE090
、
Figure 167995DEST_PATH_IMAGE091
are the ratio of pure power load in active power and reactive power respectively, and
Figure 661294DEST_PATH_IMAGE092
、
Figure 696246DEST_PATH_IMAGE093
；
the differential transformation of the algebraic equation is:
Figure 342122DEST_PATH_IMAGE094
Figure 437117DEST_PATH_IMAGE095
in the above formula, the first and second carbon atoms are,
Figure 417711DEST_PATH_IMAGE096
、
Figure 256354DEST_PATH_IMAGE097
、
Figure 881370DEST_PATH_IMAGE098
、
Figure 786747DEST_PATH_IMAGE099
、
Figure 864425DEST_PATH_IMAGE100
are respectively as
Figure 772338DEST_PATH_IMAGE101
、
Figure 376495DEST_PATH_IMAGE102
、
Figure 78871DEST_PATH_IMAGE103
、
Figure 519211DEST_PATH_IMAGE104
、
Figure 699657DEST_PATH_IMAGE105
To (1) akThe coefficient of the power series of the order,A、Bin the form of a matrix of coefficients,
Figure 299265DEST_PATH_IMAGE106
、
Figure 297177DEST_PATH_IMAGE107
is a matrix of coefficients of the generator,
Figure 349447DEST_PATH_IMAGE108
、
Figure 333583DEST_PATH_IMAGE109
is a coefficient matrix of the load, an
Figure 164530DEST_PATH_IMAGE106
、
Figure 943130DEST_PATH_IMAGE107
、
Figure 872908DEST_PATH_IMAGE110
、
Figure 395157DEST_PATH_IMAGE109
Including the front of the state variablekFront of order power series coefficient and non-algebraic variablek-power series coefficients of order 1.
4. A power system fast time domain simulation method according to any one of claims 1-3, characterized by:
the step B comprises the following steps in sequence:
step B1, inputting the initial values of the state variables and the node voltage of the power systemx 0 Andv 0 is that isX[0]、V[0]Then, the 1 st order power series coefficient of each state variable is calculated based on the differential transformation formula of the dynamic differential equation and the differential transformation formula of the algebraic equationX[1]1 st order power series coefficient of node voltageV[1]；
Step B2, loopThe loop repeats step B1 up to the orderkAnd when the maximum value is reached, obtaining each state variable and node voltage value at the time point.
CN202210829815.5A 2022-07-15 2022-07-15 Rapid time domain simulation method for electric power system Active CN114912300B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210829815.5A CN114912300B (en) 2022-07-15 2022-07-15 Rapid time domain simulation method for electric power system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210829815.5A CN114912300B (en) 2022-07-15 2022-07-15 Rapid time domain simulation method for electric power system

Publications (2)

Publication Number Publication Date
CN114912300A true CN114912300A (en) 2022-08-16
CN114912300B CN114912300B (en) 2022-09-30

Family

ID=82772808

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210829815.5A Active CN114912300B (en) 2022-07-15 2022-07-15 Rapid time domain simulation method for electric power system

Country Status (1)

Country Link
CN (1) CN114912300B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115758784A (en) * 2022-11-30 2023-03-07 南方电网数字电网研究院有限公司 Large-scale Jacobian matrix low-time-consumption iteration method for supporting time domain simulation of power system

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101446991A (en) * 2008-08-15 2009-06-03 中国电力科学研究院 Numerical integration method for electric power system full dynamic simulation
CN101651343A (en) * 2009-09-09 2010-02-17 国家电网公司 Method and system for checking electric power system model based on hybrid dynamic simulation
US20150149132A1 (en) * 2013-11-27 2015-05-28 Battelle Memorial Institute Time-stacking method for dynamic simulations

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101446991A (en) * 2008-08-15 2009-06-03 中国电力科学研究院 Numerical integration method for electric power system full dynamic simulation
CN101651343A (en) * 2009-09-09 2010-02-17 国家电网公司 Method and system for checking electric power system model based on hybrid dynamic simulation
US20150149132A1 (en) * 2013-11-27 2015-05-28 Battelle Memorial Institute Time-stacking method for dynamic simulations

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
宋新立等: "电力系统全过程动态仿真的组合数值积分算法研究", 《中国电机工程学报》 *
张鹏等: "基于谐波特性的简化Buck-boost变换器动态相量法建模与仿真", 《现代电力》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115758784A (en) * 2022-11-30 2023-03-07 南方电网数字电网研究院有限公司 Large-scale Jacobian matrix low-time-consumption iteration method for supporting time domain simulation of power system
CN115758784B (en) * 2022-11-30 2023-12-12 南方电网数字电网研究院有限公司 Large jacobian matrix low-time-consumption iteration method for supporting power system time domain simulation

Also Published As

Publication number Publication date
CN114912300B (en) 2022-09-30

Similar Documents

Publication Publication Date Title
Duan et al. Power system simulation using the multistage adomian decomposition method
Thakallapelli et al. Real-time frequency based reduced order modeling of large power grid
CN113326673B (en) VBR model electromagnetic transient simulation method and system of synchronous motor
CN114912300B (en) Rapid time domain simulation method for electric power system
CN111900718B (en) Active power distribution network dynamic simulation method based on multi-stage optimization catch-up variational iteration method
WO2018102720A1 (en) System and method for a fast power network simulator
Chen et al. Fast steady-state analysis in time-stepping finite-element simulation of induction motors based on virtual blocked rotor techniques
CN115081250A (en) Electric power system uncertainty affine power flow calculation method based on all-pure embedding
Liu et al. Fast power system dynamic simulation using continued fractions
Sambariya et al. Routh approximation: an approach of model order reduction in SISO and MIMO systems
CN111641229B (en) Wind power generation system output monitoring method and system based on extended harmonic domain model
CN110048428B (en) Power system probability load flow calculation method based on probability conservation principle
CN116722533A (en) Parameterized transient stability prevention control solving method based on random wind power prediction interval
Liang et al. Analysis of access location and capacity of distributed generation based on OpenDSS
CN112836165B (en) Transient stability network equation method based on all-pure embedding
CN114465280A (en) Dynamic equivalent modeling method for new energy grid-connected system
CN111881541B (en) Power system transient stability simulation algorithm based on discontinuous Galerkin method
CN109149645B (en) Transient stability calculation method for power grid containing double-fed induction type wind turbine generator
Bian et al. Identification and improvement of probabilistic voltage instability modes of power system with wind power integration
CN111987734A (en) Transient overvoltage two-stage optimization control method based on trajectory sensitivity
Ishchenko et al. Linearization of dynamic model of squirrel-cage induction generator wind turbine
Li et al. Matrix exponential based algorithm for electromagnetic transient modeling and simulation of large-scale induction generator wind farms
Xiong et al. Semi-Analytical Electromagnetic Transient Simulation Using Differential Transformation
Zhang et al. Study on dynamic equivalent coherency-based of Hainan power grid
Jiang et al. Hybrid Time Domain Simulation Based on Numerical Integration and Holomorphic Embedding

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant