CN109066683B - Static voltage stability analysis method considering harmonic influence - Google Patents

Static voltage stability analysis method considering harmonic influence Download PDF

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CN109066683B
CN109066683B CN201811189063.0A CN201811189063A CN109066683B CN 109066683 B CN109066683 B CN 109066683B CN 201811189063 A CN201811189063 A CN 201811189063A CN 109066683 B CN109066683 B CN 109066683B
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voltage
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CN109066683A (en
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王金浩
秦文萍
逯瑞鹏
雷达
李胜文
杨超颖
杨赟磊
张敏
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Taiyuan University of Technology
Electric Power Research Institute of State Grid Shanxi Electric Power Co Ltd
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Electric Power Research Institute of State Grid Shanxi Electric Power Co Ltd
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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
    • H02J3/01—Arrangements for reducing harmonics or ripples
    • 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
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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    • Y02E40/40—Arrangements for reducing harmonics

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Abstract

The invention belongs to the field of power grid reliability containing nonlinear loads and distributed power supplies, and relates to a method for analyzing the influence of harmonic waves on the power grid reliability, in particular to a static voltage stability analysis method for considering the influence of the harmonic waves. The invention provides a static voltage stability analysis method considering harmonic influence. Firstly, the influence of harmonic waves is considered when the critical operation state of the system is approached, and the harmonic flow of the system is solved by utilizing a decoupling method to obtain the critical operation state of the system under the influence of the harmonic waves. And secondly, two indexes of voltage sensitivity and voltage distortion sensitivity are provided, and weak nodes and sensitive nodes of the system, which are influenced by harmonic waves, are evaluated and calculated. Thirdly, the Latin hypercube sampling is used for uncertainty harmonic power flow analysis, uncertainty of linear load and nonlinear load in a system is considered, and statistical analysis is conducted on static voltage stability of the power grid.

Description

Static voltage stability analysis method considering harmonic influence
Technical Field
The invention belongs to the field of power grid reliability containing nonlinear loads and distributed power supplies, and relates to a method for analyzing the influence of harmonic waves on the power grid reliability, in particular to a static voltage stability analysis method for considering the influence of the harmonic waves.
Background
The waveform distortion problem of the power system is originally raised in germany in the second and thirty years of the last century, and in the fifth and sixty years, engineers in various countries have conducted a great deal of research on the harmonic problem of the inverter, and have obtained a great deal of research results. The eighties began, and the railway electrification in China rapidly developed, so that the obvious harmonic problem brought by the rapid development of the railway electrification becomes an important opportunity for the development of harmonic theory and technology in China. In recent years, with the diversification and development of power loads and the large number of applications of power electronic devices, the proportion of nonlinear loads to the entire load has increased year by year, and when the nonlinear loads are connected to a power system to operate, a large number of harmonics are injected into the nonlinear loads, which are the most important factors of the voltage waveform of the power system. The management of the power quality of the distribution network directly connected with the load is very challenging. In addition, due to the increasing exhaustion of fossil energy and the development and utilization of clean energy by human beings, the distributed power generation technology is vigorously developed, a power distribution network is developing towards an active power distribution network with multiple sources, flexibility and sustainable development, the pressure of the power distribution network is relieved, meanwhile, due to the characteristics of intermittence and randomness of renewable energy and a grid connection mode of a power electronic device, more power quality problems are brought to the power distribution network, and the harmonic problem is a main concern of a power operation department.
Disclosure of Invention
The invention aims to solve the problem of the influence of harmonic waves on a power system, and establishes a power system static voltage stability evaluation method considering the harmonic wave influence aiming at the problems of random fluctuation of loads, multiple harmonic wave sources of a power distribution network, random fluctuation of loads, harmonic wave sources and the like.
The invention is realized by adopting the following technical scheme: the static voltage stability analysis method considering the harmonic influence comprises an element model building method, a harmonic load flow calculation method and a static voltage stability analysis method;
the element model building and harmonic current calculating method comprises building a harmonic source model, building a power transmission line model, building a load model and solving harmonic current by using a decoupling method;
building a harmonic source model:
judging the type of a harmonic source under the condition that only one harmonic source exists in the system, if the harmonic source is a distributed power supply, regarding a node where the distributed power supply is located as a PV node when calculating fundamental wave power flow, and regarding the node where the distributed power supply is located as a balance node when calculating harmonic power flow; if the harmonic source is a nonlinear load, when the fundamental wave load flow is calculated, the node where the nonlinear load is located is regarded as a PQ node, and when the harmonic load flow is calculated, the node where the nonlinear load is located is regarded as a balance node;
if a plurality of harmonic sources exist in the system, but all the harmonic sources are nonlinear loads, when the fundamental wave power flow is calculated, a node where the nonlinear load is located is regarded as a PQ node, when the harmonic power flow is calculated, a node with the highest nonlinear load content is regarded as a balance node, and nodes where the rest nonlinear loads are located are regarded as PV nodes; if the system comprises both a distributed power supply and a nonlinear load, when the fundamental wave power flow is calculated, the node where the distributed power supply is located is regarded as a PV node, the node where the nonlinear load is located is regarded as a PQ node, when the harmonic power flow is calculated, the node where the distributed power supply with larger capacity is located is regarded as a balance node, and the nodes where the other harmonic sources are located are regarded as PV nodes; if harmonic sources in the system are all distributed power supplies, when fundamental wave power flow is calculated, nodes where the distributed power supplies are located are regarded as PV nodes, when harmonic power flow is calculated, the node where one distributed power supply with the largest capacity is located is regarded as a balance node, and the nodes where the rest distributed power supplies are located are regarded as PV nodes.
When the harmonic power flow is calculated, the situation that the power flow is not converged due to too many PV nodes in the system can occur, the harmonic power flow is grouped according to the capacity of harmonic sources and the harmonic characteristics of the harmonic sources, the harmonic source groups with similar capacity and the same harmonic characteristics are calculated in a unified mode, each harmonic source group is subjected to primary harmonic power flow calculation, and the calculation is carried out through an overlapping method.
Building a power transmission line model: the transmission line is expressed by an equivalent pi-type circuit of concentrated parameters, and the equivalent pi-type circuit parameters are simple concentration of distributed parameters, namely:
Figure BDA0001827005830000031
in the formula, yl1Is the fundamental conductance of the line, zl1Is the fundamental impedance of the line, r01、x01、b01The fundamental wave resistance, the fundamental wave reactance and the fundamental wave susceptance of the unit length of the line are respectively; l is the line length, when the current in the line is h harmonic:
Figure BDA0001827005830000032
in the formula, ZChAnd rhThe characteristic impedance and the propagation function of the line at the time of h-th harmonic are both complex numbers, and the specific calculation is as follows:
Figure BDA0001827005830000033
in the formula, yohConductance of the power system at h harmonic, yoh＝jhb01；zohImpedance of the power system at h harmonic, zoh＝hr01+jhx01；ZLhLine impedance in the case of h harmonic, YLhThe line conductance is for the h harmonic case;
building a load model: the harmonic impedance calculation is as follows:
Figure BDA0001827005830000034
Figure BDA0001827005830000035
in the formula of UiIs the actual voltage of node i, and S is the apparent power of node; rS，XSThe resistance and the reactance of the equivalent motor in fundamental wave are respectively; zshThe impedance of the load under the condition of h harmonic wave, P is the active power of the load, and Q is the reactive power of the load;
solving the harmonic power flow by using a decoupling method: (1) calculating fundamental wave power flow: the voltage U of each node of the power system is solved by iterative calculation without considering the influence of harmonic waves1iI represents each node in the power system; (2) calculating the harmonic power flow: updating electricity using harmonic source model, transmission line model and load modelThe fundamental wave voltage U of each node calculated by the fundamental wave current of the force system state1iUpdating the state of the nonlinear load in the power system by the load model of the nonlinear load, and solving the harmonic voltage U of each node in the power system in an iterative modehj(ii) a (3) Harmonic voltage U through each node in the power systemhjAnd solving the per unit value U of each node voltage by using a superposition methodhi，
Figure BDA0001827005830000041
In the formula of UhiThe method comprises the steps that a synthesized harmonic voltage per unit value at an ith node calculated for a group of considered harmonic sources is represented, and j represents a node where the harmonic source is located;
the static voltage stability analysis method comprises the steps of setting two indexes of voltage sensitivity and voltage distortion sensitivity and analyzing the static voltage stability;
two indexes of voltage sensitivity and voltage distortion sensitivity are set: index of voltage sensitivity
Figure BDA0001827005830000042
Voltage distortion sensitive index
Figure BDA0001827005830000043
Wherein the actual voltage at node i is UiAnd the voltage variation of the node i caused by the harmonic wave is delta UiThe voltage sensitivity index α 1 indicates a case where the harmonic influence is not considered in the power system including the harmonic source, and the voltage distortion sensitivity α 2 indicates a case where the harmonic influence is considered in the power system including the harmonic source, and the voltage value
Figure BDA0001827005830000044
Amount of voltage change
Figure BDA0001827005830000045
Figure BDA0001827005830000046
In the formula, THDuiRepresenting the rate of voltage distortion at node i;
the voltage sensitivity index α 1 can be transformed into
Figure BDA0001827005830000047
The voltage distortion sensitivity index α 2 can be deformed to
Figure BDA0001827005830000051
Indexes alpha 1 and alpha 2 only correspond to voltage distortion rates THDu of all nodesiThe influence of harmonic waves on the static voltage stability of the power system can be reflected;
static voltage stability analysis:
the invention provides a static voltage stability identification method for combining weak nodes, security domains and sensitive nodes based on a voltage sensitivity index and a voltage distortion sensitivity index, and the identification process is simple and easy to realize.
The smaller the voltage sensitivity index and the voltage distortion sensitivity index are, the weaker the node is.
Partitioning the system according to a line structure, partitioning a security domain of a partitioned area through a voltage sensitivity index and a voltage distortion sensitivity index, and if no voltage risk exists, determining the system to be a security domain; if there is a voltage risk in certain operating modes, it is a warning zone, if there is a voltage risk, it is a limiting zone.
The ratio alpha 1/alpha 2 of the voltage distortion sensitivity index to the voltage sensitivity index is THDu, which reflects the voltage distortion rate of the node, so that the sensitive node of the system to the harmonic wave can be judged.
The weak node concerns the part which is easy to crash in the system critical operation state; the security domain emphasizes the overall state of the system in the critical operation state of the system; the sensitive nodes pay attention to the influence of the harmonic waves on the nodes, and the weak nodes, the security domain and the sensitive nodes are combined, so that the influence of the harmonic waves on the system can be better described.
The method comprises the steps of introducing Latin hypercube sampling into harmonic load flow calculation, generating a plurality of groups of initial load matrixes, simultaneously considering random fluctuation of linear loads and uncertainty of nonlinear loads, solving the stability of the static voltage of a system for each initial load matrix, and reducing the influence of the initial loads on the stability of the static voltage of the system;
by utilizing a decoupling method and an improved binary search method, under the condition of a state m determined by the access position and the initial load of a harmonic source, the node voltage U of the power system in the critical state of the state m under the condition of considering the harmonic influence is obtainediAnd voltage distortion rate THDuiAnd further obtaining a voltage sensitivity index alpha 1 and a voltage distortion sensitivity index alpha 2 in the critical state, wherein the lowest numerical values of the voltage sensitivity index alpha 1 and the voltage distortion sensitivity index alpha 2 are weak nodes of the power system in the critical state of the state M, the voltage sensitivity index alpha 1 and the voltage distortion sensitivity index alpha 2 of each node in the power system form a security domain of the power system in the critical state of the state M, the sensitive node is a node with the largest influence of harmonic content change on the static voltage stability of the system, all the states M are analyzed, all the M states are analyzed, the weak nodes, the security domain and the sensitive nodes of the system in different states are analyzed statistically, and the static voltage stability of the system is further analyzed.
Compared with the existing research, the beneficial effects of the invention are as follows:
(1) in the current research, the research on the harmonic waves is under the normal operation condition of the system, and the critical operation state is not considered. The method considers the influence of harmonic waves when approaching the critical operation state of the system, and solves the harmonic flow of the system by using a decoupling method to obtain the critical operation state of the system under the influence of the harmonic waves.
(2) In the current research, a voltage stability analysis method comprises a point-by-point method and a safety domain method, the point-by-point method is difficult to provide overall evaluation for the operation state of the power system, and the safety domain method does not consider harmonic influence.
(3) In the current research, the uncertainty of the harmonic source is considered in the literature, but the uncertainty of the harmonic source and the linear load is not considered at the same time. According to the method, Latin hypercube sampling is used for uncertainty harmonic power flow analysis, uncertainty of linear load and nonlinear load in a system is considered, and statistical analysis is carried out on static voltage stability of a power grid.
(4) The method combines a harmonic power flow calculation method with an improved binary search method, takes the influence of harmonic waves on voltage stability into consideration, reduces the calculation amount, and improves the calculation speed.
Drawings
FIG. 1 is a flow chart of the decoupling method for calculating the harmonic power flow.
FIG. 2 is a flow chart of a static voltage stability analysis method taking harmonic effects into account according to the present invention.
Fig. 3 is a wiring diagram of an IEEE33 node system used in the present invention.
FIG. 4 is a bar chart of the single harmonic source voltage sensitivity index of the present invention.
FIG. 5 is a bar graph of the single harmonic source voltage distortion sensitivity index of the present invention.
FIG. 6 is a comparison of the results of the voltage sensitivity index and the voltage distortion sensitivity index for a multiple harmonic source of the present invention.
FIG. 7 is a voltage sensitivity distribution curve under the threshold condition of static voltage instability of the system of the present invention.
FIG. 8 is a voltage distortion sensitivity distribution curve under the critical state of static voltage instability of the system of the present invention.
FIG. 9 is a partial distribution curve of voltage sensitivity under the threshold condition of static voltage instability of the system of the present invention.
FIG. 10 is a partial distribution curve of voltage sensitivity under the threshold condition of static voltage instability of the system of the present invention.
Detailed Description
The invention provides a static voltage stability analysis method considering harmonic influence. Firstly, the influence of harmonic waves is considered when the critical operation state of the system is approached, and the harmonic flow of the system is solved by utilizing a decoupling method to obtain the critical operation state of the system under the influence of the harmonic waves. And secondly, two indexes of voltage sensitivity and voltage distortion sensitivity are provided, and weak nodes and sensitive nodes of the system, which are influenced by harmonic waves, are evaluated and calculated. Thirdly, the Latin hypercube sampling is used for uncertainty harmonic power flow analysis, uncertainty of linear load and nonlinear load in a system is considered, and statistical analysis is conducted on static voltage stability of the power grid. The specific scheme is as follows:
element model and harmonic power flow calculation
The harmonic current calculation is an important means for researching the harmonic problem in the power flow, the distribution condition of the full-network harmonic current can be known through the harmonic current calculation, the harmonic indexes of all nodes are obtained, and the harmonic current calculation is an important basis for evaluating the stability of the power system. The combination of all element states is the power flow, so in the harmonic power flow calculation, it is most important to set the harmonic parameters, models and connection conditions of each element of the power supply system, and the following discusses the calculation methods of the harmonic parameters and the harmonic power flow of each element.
Harmonic source model
In the power system, harmonic sources mainly include two types, one is traditional nonlinear equipment such as an arc furnace, and the other is modern power electronic nonlinear equipment such as an electric vehicle charging pile and a distributed power supply. Table 1 shows the harmonic content of the electric vehicle charging pile, and table 2 shows the harmonic content of the electric arc furnace.
TABLE 1 electric vehicle charging pile subharmonic current content
Tab 1 The content of each harmonic current in charging piles of electric vehicles
Figure BDA0001827005830000081
TABLE 2 electric arc furnace subharmonic content
Tab 2 All harmonic content of EAF
Figure BDA0001827005830000082
Figure BDA0001827005830000091
Mathematically, the harmonic sources may be unified as a function of the node voltage and the compliance control parameter as shown in equation (1), and the resulting harmonic currents may be obtained by the equation: i ish＝fh(U1j,U2j,…,UHj,C1,C2,…,CH) H is 1,2, …, and (1) wherein, IhIs the h-th harmonic current, U, generated by the harmonic source1j,U2j,…,UHjIn the case of the harmonic source injection node, the fundamental voltage and each harmonic voltage, C, of the node j1,C2,…,CHIs a control parameter of the harmonic source, and H is the maximum number of harmonics. Theoretically, the function can calculate accurate harmonic information, but the function is not suitable for actual power systems with various harmonic sources due to the need of respectively modeling different harmonic sources and complex calculation.
Therefore, for the processing of the harmonic source, the type of the harmonic source is judged under the condition that there is only one harmonic source in the system, if the harmonic source is a distributed power supply, a node where the distributed power supply is located is regarded as a PV node when the fundamental wave power flow is calculated, and the node where the distributed power supply is located is regarded as a balance node when the harmonic power flow is calculated; if the harmonic source is a nonlinear load, when the fundamental wave load flow is calculated, the node where the nonlinear load is located is regarded as a PQ node, and when the harmonic load flow is calculated, the node where the nonlinear load is located is regarded as a balance node;
if a plurality of harmonic sources exist in the system, but all the harmonic sources are nonlinear loads, when the fundamental wave power flow is calculated, a node where the nonlinear load is located is regarded as a PQ node, when the harmonic power flow is calculated, a node with the highest nonlinear load content is regarded as a balance node, and nodes where the rest nonlinear loads are located are regarded as PV nodes; if the system comprises both a distributed power supply and a nonlinear load, when the fundamental wave power flow is calculated, the node where the distributed power supply is located is regarded as a PV node, the node where the nonlinear load is located is regarded as a PQ node, when the harmonic power flow is calculated, the node where the distributed power supply with larger capacity is located is regarded as a balance node, and the nodes where the other harmonic sources are located are regarded as PV nodes; if harmonic sources in the system are all distributed power supplies, when fundamental wave power flow is calculated, nodes where the distributed power supplies are located are regarded as PV nodes, when harmonic power flow is calculated, the node where one distributed power supply with the largest capacity is located is regarded as a balance node, and the nodes where the rest distributed power supplies are located are regarded as PV nodes.
The superposition rule of the h-th synthesized harmonic voltage can be calculated according to equation (2):
Figure BDA0001827005830000101
in the formula of UhiRepresents the synthetic harmonic voltage value at the (h) th node calculated for a set of harmonic sources (probability statistics) under consideration; u shapehjFor the value of the single harmonic voltage (h) to be synthesized, j represents the node at which the harmonic source is located.
TABLE 3 overlay index. varies:
Tab 3 Overlay Index∝
Figure BDA0001827005830000102
transmission line model
The transmission line is represented by an equivalent pi-type circuit of concentrated parameters, and the equivalent circuit parameters are usually simple concentration of distributed parameters, namely:
Figure BDA0001827005830000103
in the formula, r01、x01、b01The fundamental wave resistance, the reactance and the susceptance of the unit length of the line are respectively; l is the line length, when the current in the line is h harmonic:
Figure BDA0001827005830000104
in the formula, ZchAnd rhThe characteristic impedance and the propagation function of the line at the time of h-th harmonic are both complex numbers, and the specific calculation is as follows:
Figure BDA0001827005830000105
in the formula, yohAt h harmonic, the conductance of the system, yoh＝jhb01；zohAt h harmonic, the impedance of the system, zoh＝hr01+jhx01。
Load model
The load includes a normal linear load and a nonlinear load. Considering the influence of the random fluctuation factor of the load on the power system, the load adopts normal distribution, the given numerical value of the system is taken as a mean value, and the variance is 0.05, so as to obtain the random load state of each node of the system.
Considering the skin effect, the influence of the harmonic wave on the transmission line is not negligible, and the harmonic impedance is calculated as shown in formulas (6) to (7):
Figure BDA0001827005830000111
Figure BDA0001827005830000112
in the formula of UiIs the actual voltage at node i; s is the apparent power of the node; rS，XSThe values are the resistance and reactance of the motor at the fundamental wave.
Method for solving harmonic power flow by using decoupling method
In an electric power system, generally, the harmonic wave is smaller than the fundamental wave, so the fundamental wave power flow is basically not influenced by the harmonic wave power flow. The decoupling method utilizes this point, simplifies the solution, and the solution idea is as follows:
(1) calculating fundamental wave power flow: the voltage U of each node of the power system is solved by iterative calculation without considering the influence of harmonic waves1i；
(2) Calculating the harmonic power flow: calculating the voltage U of each node by using the fundamental flow according to the new system state by using the harmonic source model, the transmission line model and the load model1iAnd load model of nonlinear loadUpdating the state of the nonlinear load in the system, and solving the harmonic voltage U of each node in the system in an iterative mannerhj；
(3) Harmonic voltage U of each node generated by typical harmonic source in the systemhjAnd solving the per unit value U of each node voltage by using a superposition methodhiAnd calculating the voltage and the voltage distortion rate of each node in the system under the influence of harmonic waves.
The flow chart is shown in fig. 1.
The "safety and stability of power system" defines voltage stability as the ability of a power system to remain or recover within an allowable range without voltage collapse after small or large disturbances are applied to the power system. The harmonic wave can be regarded as disturbance of the power system, and in the process of power electronization of the power system, it is necessary to study the influence of the harmonic wave on the voltage stability of the power system.
Static voltage stability analysis method considering harmonic influence
The influence of harmonic waves on a power system is mainly embodied in two aspects, namely, a nonlinear load and a distributed power supply are used as harmonic wave sources, and node voltage can be raised; secondly, the node voltage distortion rate will be greatly increased, which affects the normal operation of the device.
The node breakdown voltage refers to the voltage level of the node when the system is operating critically. The breakdown voltage can reflect the strength of the node to a certain extent, and theoretically, the higher the breakdown voltage is, the stronger the node is, because the voltage level of the node can still be kept relatively normal when the system is operated critically.
The degree of voltage waveform distortion is measured by the voltage sinusoidal wave distortion rate, also known as the voltage harmonic distortion rate. The voltage harmonic distortion rate is expressed as a percentage of the ratio of the root mean square value of each harmonic voltage to the effective value of the fundamental voltage:
Figure BDA0001827005830000121
in the formula, THDuiRepresenting the voltage distortion rate, U, of node i1iBase representing node iWave voltage, UhiRepresenting the h harmonic voltage at node i.
The sensitivity index is a state index, can reflect the characteristic of a certain running state of the system, and can be obtained by approaching the system to a critical state of impending voltage instability, so that the sensitivity of each node voltage in the power grid when the system is close to the voltage instability can be reflected, and the sensitivity of each node in the power grid to interference can be more accurately reflected.
In order to consider the influence of harmonic waves on the stability of the static voltage of the system in a power grid containing a harmonic wave source, a voltage sensitivity index and a voltage distortion sensitivity index are provided, and the influence of a voltage distortion rate on the stability of the static voltage of the system is reflected. The index is defined as follows:
voltage sensitivity index α 1:
Figure BDA0001827005830000131
voltage distortion sensitivity index α 2:
Figure BDA0001827005830000132
wherein the actual voltage at node i is Ui(ii) a Voltage change of node i caused by harmonics to DeltaUiThe voltage sensitivity index α 1 indicates that the harmonic influence is not considered in a system including a harmonic source, and the voltage distortion sensitivity α 1 indicates that the harmonic influence is considered in a system including a harmonic source. Value of voltage
Figure BDA0001827005830000133
Amount of voltage change
Figure BDA0001827005830000134
Then:
voltage sensitivity index:
Figure BDA0001827005830000135
the voltage distortion sensitivity index is:
Figure BDA0001827005830000136
indexes α 1, α 2 are defined as voltage distortion rates THDu corresponding to the respective nodes onlyiIn connection with this, the effect of harmonics on the static voltage stability of the power system can be reflected. Obviously, the larger the voltage sensitivity index and the voltage distortion sensitivity index, the less likely the node will collapse.
Static voltage stability analysis method calculation step considering harmonic influence
Considering the change of nonlinear load and the random fluctuation of linear load in the system, the Latin hypercube sampling is introduced into the harmonic load flow calculation, and the node voltage U of the system in a certain critical state can be obtained through multiple calculations by utilizing a decoupling method and an improved binary search methodiAnd voltage distortion rate THDuiThe voltage sensitivity index alpha 1 and the voltage distortion sensitivity index alpha 2 statistically analyze the influence of harmonic waves on the static voltage stability of the system, and obtain weak nodes, safety domains and sensitive nodes of the system considering the influence of the harmonic waves; the sensitive node reflects the influence of the harmonic content change on the static voltage stability of the system.
The security domain method is a method developed on the basis of a point-by-point method, and the security domain method considers problems from the aspect of domains and describes an overall region capable of safely and stably running.
Taking the IEEE33 node system as an example, simulation analysis was performed using MATLAB software. Under the influence of harmonic waves, the condition that the system comprises one harmonic wave source and a plurality of harmonic wave sources is simulated in sequence, and the security domain of the system is obtained.
Compared with fig. 4, in fig. 5, the weak nodes are increased, the probability that the 18 nodes become weak nodes is decreased, and the probability that the 18 nodes become weak nodes is increased, which shows that the 18 nodes are more sensitive to system harmonics.
As can be seen from fig. 6, the probability that the 18 node becomes a weak node increases, and the probability that the 33 node becomes a weak node decreases, so that the 18 node is sensitive to system harmonics.
Comparing fig. 7 and fig. 8, the trend of the two changes is approximately the same, which illustrates that the weak nodes and the security domains in the system do not change when the harmonics are considered and not considered.
In fig. 9, the voltage sensitivity indexes of the node 18 and the node 33 are relatively close; in fig. 10, the voltage distortion sensitivity index of the 18 node is obviously smaller than that of the 33 node, which indicates that the probability that the 18 node becomes a weak node of the system is increased under the condition of considering the harmonic wave, and indicates that the 18 node is sensitive to the harmonic wave change of the system.

Claims (1)

1. The static voltage stability analysis method considering the harmonic influence is characterized by comprising an element model building method, a harmonic load flow calculation method and a static voltage stability analysis method;
the element model building and harmonic current calculating method comprises building a harmonic source model, building a power transmission line model, building a load model and solving harmonic current by using a decoupling method;
building a harmonic source model: judging the type of a harmonic source under the condition that only one harmonic source exists in the system, if the harmonic source is a distributed power supply, regarding a node where the distributed power supply is located as a PV node when calculating fundamental wave power flow, and regarding the node where the distributed power supply is located as a balance node when calculating harmonic power flow; if the harmonic source is a nonlinear load, when the fundamental wave load flow is calculated, the node where the nonlinear load is located is regarded as a PQ node, and when the harmonic load flow is calculated, the node where the nonlinear load is located is regarded as a balance node;
if a plurality of harmonic sources exist in the system, but all the harmonic sources are nonlinear loads, when the fundamental wave power flow is calculated, a node where the nonlinear load is located is regarded as a PQ node, when the harmonic power flow is calculated, a node with the highest nonlinear load content is regarded as a balance node, and nodes where the rest nonlinear loads are located are regarded as PV nodes; if the system comprises both a distributed power supply and a nonlinear load, when the fundamental wave power flow is calculated, the node where the distributed power supply is located is regarded as a PV node, the node where the nonlinear load is located is regarded as a PQ node, when the harmonic power flow is calculated, the node where the distributed power supply with larger capacity is located is regarded as a balance node, and the nodes where the other harmonic sources are located are regarded as PV nodes; if harmonic sources in the system are all distributed power supplies, when fundamental wave power flow is calculated, nodes where the distributed power supplies are located are regarded as PV nodes, when harmonic power flow is calculated, the node where one distributed power supply with the largest capacity is located is regarded as a balance node, and the nodes where the other distributed power supplies are located are regarded as PV nodes;
building a power transmission line model: the transmission line is expressed by an equivalent pi-type circuit of concentrated parameters, and the equivalent pi-type circuit parameters are simple concentration of distributed parameters, namely:
Figure FDA0001827005820000021
in the formula, r01、x01、b01The fundamental wave resistance, the fundamental wave reactance and the fundamental wave susceptance of the unit length of the line are respectively; l is the line length, when the current in the line is h harmonic:
Figure FDA0001827005820000022
in the formula, ZChAnd rhThe characteristic impedance and the propagation function of the line at the time of h-th harmonic are both complex numbers, and the specific calculation is as follows:
Figure FDA0001827005820000023
in the formula, yohConductance of the power system at h harmonic, yoh＝jhb01；zohImpedance of the power system at h harmonic, zoh＝hr01+jhx01；
Building a load model: the harmonic impedance calculation is as follows:
Figure FDA0001827005820000024
Figure FDA0001827005820000025
in the formula of UiIs the actual voltage at node i; apparent power of S as node；RS，XSThe resistance and the reactance of the equivalent motor in fundamental wave are respectively;
solving the harmonic power flow by using a decoupling method: (1) calculating fundamental wave power flow: the voltage U of each node of the power system is solved by iterative calculation without considering the influence of harmonic waves1iI represents each node in the power system; (2) calculating the harmonic power flow: updating the state of the power system by using a harmonic source model, a transmission line model and a load model, and calculating the fundamental voltage U of each node by using the fundamental current1iUpdating the state of the nonlinear load in the power system by the load model of the nonlinear load, and solving the harmonic voltage U of each node in the power system in an iterative modehj(ii) a (3) Harmonic voltage U through each node in the power systemhjAnd solving the per unit value U of each node voltage by using a superposition methodhi，
Figure FDA0001827005820000026
In the formula of UhiThe method comprises the steps that a synthesized harmonic voltage per unit value at an ith node calculated for a group of considered harmonic sources is represented, and j represents a node where the harmonic source is located;
the static voltage stability analysis method comprises the steps of setting two indexes of voltage sensitivity and voltage distortion sensitivity and analyzing the static voltage stability;
two indexes of voltage sensitivity and voltage distortion sensitivity are set: index of voltage sensitivity
Figure FDA0001827005820000031
Voltage distortion sensitive index
Figure FDA0001827005820000032
Wherein the actual voltage at node i is UiAnd the voltage variation of the node i caused by the harmonic wave is delta UiThe voltage sensitivity index α 1 indicates a case where the harmonic influence is not considered in the power system including the harmonic source, and the voltage distortion sensitivity α 2 indicates a case where the harmonic influence is considered in the power system including the harmonic source, and the voltage value
Figure FDA0001827005820000033
Amount of voltage change
Figure FDA0001827005820000034
Figure FDA0001827005820000035
In the formula, THDuiRepresenting the rate of voltage distortion at node i; the voltage sensitivity index α 1 can be transformed into
Figure FDA0001827005820000036
The voltage distortion sensitivity index α 2 can be deformed to
Figure FDA0001827005820000037
Indexes alpha 1 and alpha 2 only correspond to voltage distortion rates THDu of all nodesiThe influence of harmonic waves on the static voltage stability of the power system can be reflected;
static voltage stability analysis: the method comprises the steps of introducing Latin hypercube sampling into harmonic load flow calculation, generating a plurality of groups of initial load matrixes, simultaneously considering random fluctuation of linear loads and uncertainty of nonlinear loads, solving the stability of the static voltage of a system for each initial load matrix, and reducing the influence of the initial loads on the stability of the static voltage of the system;
by utilizing a decoupling method and an improved binary search method, under the condition of a state m determined by the access position and the initial load of a harmonic source, the node voltage U of the power system in the critical state of the state m under the condition of considering the harmonic influence is obtainediAnd voltage distortion rate THDuiAnd further obtaining a voltage sensitivity index alpha 1 and a voltage distortion sensitivity index alpha 2 in the critical state, wherein the lowest numerical values of the voltage sensitivity index alpha 1 and the voltage distortion sensitivity index alpha 2 are weak nodes of the power system in the critical state m, the voltage sensitivity index alpha 1 and the voltage distortion sensitivity index alpha 2 of each node in the power system form a security domain of the power system in the critical state m, and the sensitive node is the security domain of the power system in the critical state m, which is most influenced by the harmonic content change on the static voltage stability of the systemAnd the large node analyzes all the states M, finishes all the analysis of the M states, statistically analyzes weak nodes, security domains and sensitive nodes of the system in different states, and further analyzes the stability of the static voltage of the system.
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