CN109617079B - Method for analyzing existence and stability of tidal current solution of direct-current power distribution system - Google Patents

Method for analyzing existence and stability of tidal current solution of direct-current power distribution system Download PDF

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CN109617079B
CN109617079B CN201811549770.6A CN201811549770A CN109617079B CN 109617079 B CN109617079 B CN 109617079B CN 201811549770 A CN201811549770 A CN 201811549770A CN 109617079 B CN109617079 B CN 109617079B
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刘尧
管霖
郑建平
谭喆
陈建福
杨昆
柳张杰
裴星宇
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South China University of Technology SCUT
Zhuhai Power Supply Bureau of Guangdong Power Grid Co Ltd
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    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract

The invention belongs to the technical field of electric power operation, and particularly relates to a method for analyzing existence and stability of a tidal current solution of a direct-current power distribution system, which comprises the following steps: direct current power distribution systemCarrying out equivalent topology to obtain a transmission network admittance matrix Y; obtaining the current injected into the power transmission network by each node; when the converter is in droop control, calculating output voltage us(ii) a Based on the output voltage uSObtaining a steady-state working point expression of the direct current distribution system and a power flow equation of the direct current distribution system by the expression of the voltage-current characteristic of the constant power load; and calculating a power flow solution by adopting an iterative algorithm in combination with a sufficient condition T of feasible solution of the direct-current power distribution system. Based on the numerical system existence condition, the method can quickly evaluate the tide solution existence of the system after load access and voltage mutation, and acquire the running state of the direct current power distribution system; in addition, the invention fully utilizes the self characteristics of the circuit system, provides a method based on the closed-cell set theorem and obtains the condition of the existence of the power flow solution with lower conservation.

Description

Method for analyzing existence and stability of tidal current solution of direct-current power distribution system
Technical Field
The invention relates to the technical field of electric power operation, in particular to a method for analyzing existence and stability of a tidal current solution of a direct-current power distribution system.
Background
With the increase of direct current power supplies such as photovoltaic power supplies and energy storage batteries and direct current load proportion of electric vehicles and data service stations, the application requirements of direct current power distribution systems are getting larger and larger. At present, the domestic research on the power distribution network mainly focuses on the alternating current power distribution network, and compared with the alternating current power distribution network, the direct current power distribution network has the following advantages: the conversion links are few, the conversion loss rate is low and the reliability is high; no reactive power exists, and the transmission efficiency is high; the frequency synchronization problem does not exist, and the renewable energy source grid connection and the system stability are easier to realize. As a result, dc power distribution systems are becoming more widely used.
In DC power distribution systems, the load is typically connected to the DC bus by a DC/DC or DC/AC converter. When the response of the load-side converter is fast, the whole load presents a negative impedance characteristic, and the load can be equivalent to a constant-power load. In order to ensure that a direct current power distribution system can stably and reliably operate, the voltage stability is very important. Currently, most of the stability studies on the dc power distribution system focus on the small signal stability of the system, i.e. the stability near the operating point, and a corresponding stabilization control strategy is proposed. However, when the dc distribution system is large in scale, heavily loaded and has high line impedance, the system may lose the balance point with the increase of the load due to the line loss, thereby causing voltage collapse, and the voltage stability cannot be controlled by the above method.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for analyzing the existence and stability of a power flow solution of a direct-current power distribution system in a droop control mode, so that the existence condition of the power flow solution with low conservation is obtained, and the feasible existence of the power flow solution of the system after load access and voltage mutation is quickly evaluated.
In order to solve the technical problems, the invention adopts the technical scheme that:
providing a method for analyzing existence and stability of a tidal current solution of a direct current power distribution system, wherein the direct current power distribution system is of a mesh structure consisting of n converter nodes and m load nodes, the converter nodes are connected with the load nodes, and adjacent load nodes are electrically connected; the analysis method comprises the following steps:
s10, carrying out equivalent topology on the direct current distribution system by using a graph theory to obtain a power transmission network admittance matrix Y; obtaining the injection output of each node according to ohm's lawElectric current [ i ] of an electric networks,iL]TWherein isIs the output current of the converter node iLInjecting a current into the network for the load node;
s20, when the converter is in droop control, calculating to obtain an output voltage usThe expression of (1);
s30. based on the output voltage uSObtaining a steady-state working point expression of the direct current distribution system and a power flow equation of the direct current distribution system by the expression of the voltage-current characteristic of the constant power load;
and S40, calculating a power flow solution by adopting an iterative algorithm in combination with a sufficient condition T of the feasible solution of the direct-current power distribution system.
The method for analyzing the existence and stability of the power flow solution of the direct-current power distribution system is carried out in a droop control mode, and comprises the steps of establishing a power flow mathematical model of the direct-current power distribution system and obtaining sufficient conditions of feasible solution of the power flow of the system through a closed interval set theorem. And substituting the reference voltage matrix, the maximum load parameter matrix and the line parameter matrix into sufficient conditions to judge the existence of the feasible solution of the power flow. The analysis method can quickly calculate the load flow solution of the large-scale complex network, avoids the problem of nonlinear continuous load flow solution of the scale, has no specific requirement on the system structure, has wide application range and simplified calculation process, and can effectively analyze the stability of the complex direct current micro-grid; in addition, the invention rapidly evaluates the load access and the load flow solution existence of the system after voltage mutation through an iterative algorithm, can reduce the existence condition and the conservatism, and can calculate the upper limit of the load more accurately.
Preferably, in step S10, the current [ i ] of the power transmission networks,iL]TIs obtained by the following steps:
Figure GDA0002244709580000021
in the formula uSIs the output voltage of the converter node; u. ofLThe voltage of the network is injected for the load node.
Preferably, in step S20, the voltage u is outputSBy the following methodObtaining the formula:
uS＝V*-KiS(2)
in the formula V*＝[v1v2L vn]T，viIs the reference voltage of the converter; the equivalent physical meaning of K is the virtual resistance in ohms.
Preferably, in step S30, the current-voltage characteristic of the constant-power load is expressed by:
uiii＝-Pi,i∈{n+1,n+2,L,n+m} (3)
preferably, in step S30, the steady-state operating point of the dc power distribution system is obtained by:
Figure GDA0002244709580000022
Figure GDA0002244709580000023
Y1＝YLL-YLS(YSS+K-1)-1YSL
preferably, in step S30, the power flow equation of the dc power distribution system is expressed as:
ULY1uL+ULβ+P＝0m(5)
in the formula of ULP is the load voltage and the load power of the dc distribution system.
If the steady-state working point expression of the system has a real number solution, the system has a balance point, namely, a feasible power flow solution. The problem studied by the present invention can be described as: setting proper converter reference voltage V under the condition that the line parameter matrix Y and the maximum load parameter P of the system are determined*Ensuring that a trend feasible solution exists in the system; reference voltage V at converter*And under the condition that the line parameter matrix Y is determined, calculating the maximum value of the load power P which can be borne by the system on the premise of ensuring that the system has a feasible solution of the power flow.
Preferably, in step S40, the power flow solution exists when the dc power distribution system satisfies the following condition:
(1) if there is one positive column vector ξ satisfying:
0m＜ξ＜f(ξ) (6)
then there is a unique column vector x*Satisfies f (x)*)＝x*And ξ < x*＜1m；
(2) For any given system parameter V*Y and P if there is a positive vector ξ satisfying:
formula (5) exists
Figure GDA0002244709580000032
And is
Figure GDA0002244709580000033
Wherein:
Figure GDA0002244709580000034
Figure GDA0002244709580000035
function fij(q) is defined as follows:
Figure GDA0002244709580000036
preferably, if the power flow solution exists in the dc power distribution system, step S40 may be according to xn+1＝f(xn),x1＝1mAnd solving a power flow solution through an iterative algorithm.
Preferably, in step S40, the sufficient condition T for the feasible solution of the dc power distribution system is represented as:
Figure GDA0002244709580000037
where ζ is the open circuit voltage of the DC distribution system, Y1 -1For the equivalent impedance matrix of the transmission network, χ and θ are matrices (diag { ζ } Y), respectively1diag{ζ})-1The Perron eigenvalues and corresponding eigenvectors of Θ,
Figure GDA0002244709580000039
θ＝min{θ}。
compared with the prior art, the invention has the beneficial effects that:
(1) the invention fully utilizes the self characteristics of the circuit system, provides a method based on the closed-cell set theorem, and obtains the condition of existence of the tidal current solution with lower conservation;
(2) the uniqueness of the power flow solution is proved according to the nature of the limit, and an iterative algorithm of the power flow solution is given;
(3) according to the invention, an analytic and numerical-type-based system existence condition is obtained, and the feasible solution existence of the load access and the power flow of the system after voltage mutation can be rapidly evaluated according to the analytic condition; according to the numerical conditions, the conservative property of the existing conditions can be reduced, and more accurate load upper limit can be calculated.
Drawings
Fig. 1 is an equivalent topology diagram of a dc power distribution system according to a second embodiment.
Fig. 2 is a schematic view of an iterative simulation of the first embodiment to the fourth embodiment.
Fig. 3 is a schematic view of an iterative simulation of example five and example six in the second embodiment.
Detailed Description
The present invention will be further described with reference to the following embodiments. Wherein the showings are for the purpose of illustration only and are shown by way of illustration only and not in actual form, and are not to be construed as limiting the present patent; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
Example one
Providing a method for analyzing existence and stability of a tidal current solution of a direct current power distribution system, wherein the direct current power distribution system is of a mesh structure consisting of n converter nodes and m load nodes, the converter nodes are connected with the load nodes, and adjacent load nodes are electrically connected; the analysis method comprises the following steps:
s10, carrying out equivalent topology on the direct current distribution system by using a graph theory to obtain a power transmission network admittance matrix Y; according to ohm's law, the current [ i ] injected into the power transmission network by each node is obtaineds,iL]TWherein isIs the output current of the converter node iLInjecting a current into the network for the load node;
s20, when the converter is in droop control, calculating to obtain an output voltage usThe expression of (1);
s30. based on the output voltage uSObtaining a steady-state working point expression of the direct current distribution system and a power flow equation of the direct current distribution system by the expression of the voltage-current characteristic of the constant power load;
and S40, calculating a power flow solution by adopting an iterative algorithm in combination with a sufficient condition T of the feasible solution of the direct-current power distribution system.
In step S10, the current [ i ] of the power transmission networks,iL]TIs obtained by the following steps:
Figure GDA0002244709580000051
in the formula uSIs the output voltage of the converter node; u. ofLThe voltage of the network is injected for the load node.
In step S20, the output voltage uSObtained by the following method:
uS＝V*-KiS(2)
in the formula V*＝[v1v2L vn]T，viIs the reference voltage of the converter; the equivalent physical meaning of K is the virtual resistance in ohms.
In step S30, the current-voltage characteristic of the constant-power load is expressed by the following manner:
uiii＝-Pi,i∈{n+1,n+2,L,n+m} (3)
the steady-state working point of the direct-current power distribution system is obtained by the following steps:
Figure GDA0002244709580000052
Figure GDA0002244709580000053
Y1＝YLL-YLS(YSS+K-1)-1YSL
the power flow equation of the direct current power distribution system is expressed as:
ULY1uL+ULβ+P＝0m(5)
in the formula of ULP is the load voltage and the load power of the dc distribution system.
If the steady-state working point expression of the system has a real number solution, the system has a balance point, namely, a feasible power flow solution. The problem studied by the present invention can be described as: setting proper converter reference voltage V under the condition that the line parameter matrix Y and the maximum load parameter P of the system are determined*Ensuring that a trend feasible solution exists in the system; reference voltage V at converter*And under the condition that the line parameter matrix Y is determined, calculating the maximum value of the load power P which can be borne by the system on the premise of ensuring that the system has a feasible solution of the power flow.
In step S40, when the dc distribution system satisfies the following conditions, a power flow solution exists:
(1) if there is one positive column vector ξ satisfying:
0m＜ξ＜f(ξ) (6)
then there is a unique column vector x*Satisfies f (x)*)＝x*And ξ < x*＜1m；
(2) For any given system parameter V*Y and P if there is a positive vector ξ satisfying:
formula (5) exists
Figure GDA0002244709580000055
And isWherein:
Figure GDA0002244709580000061
Figure GDA0002244709580000062
function fij(q) is defined as follows:
Figure GDA0002244709580000063
if the DC power distribution system has a power flow solution, step S40 can be performed according to xn+1＝f(xn),x1＝1mAnd solving a power flow solution through an iterative algorithm.
The sufficient condition T of the feasible solution of the dc power distribution system of the present embodiment is represented as:
Figure GDA0002244709580000064
where ζ is the open circuit voltage of the DC distribution system, Y1 -1For the equivalent impedance matrix of the transmission network, χ and θ are matrices (diag { ζ } Y), respectively1diag{ζ})-1The Perron eigenvalues and corresponding eigenvectors of Θ,
Figure GDA0002244709580000065
Figure GDA0002244709580000066
θ＝min{θ}。
example two
The embodiment is an application embodiment of the first embodiment, a direct current distribution system comprising 10 converters and 20 loads is built, the nodes of the converters are marked with numbers 1-10, the nodes of the loads are marked with numbers 11-20, and the resistors between the nodes of the converters and the nodes of the loads and the resistors between the nodes of the loads are marked in fig. 1. This example provides six examples and a comparative example:
the first calculation example: the maximum load vector of the DC power distribution system is assumed to be Pmax＝104[10 10 10 10 10 8 8 8 88 10 10 10 10 10 10 12 12 12 12]TW, taking the sag coefficient as k1＝k2＝…＝k 102. Then, when the voltage of the converter satisfies equation (7), the system has a power flow feasible solution. Get v1＝v2＝…＝v10＝2463V。
Example two: the maximum load vector is the same as the first example, take v1＝v2＝2463V,v3＝v4L＝v10＝2455V。
Example three: the maximum load vector of the DC power distribution system is assumed to be Pmax＝104[15 11 10 11 11 7 8 10 87 11 14 9 10 8 7 6 10 14 11]TW, taking the sag coefficient as k1＝k2＝…＝k 102. Likewise, when the reference voltage satisfies condition (7), a trend feasible solution exists for the system. Get v1＝v2＝…＝v10＝2096V。
Example four: the maximum load vector is the same as in example three, take v1＝v2＝…＝v10＝2093V。
Fifth example of calculation: assume that the dc distribution system load varies as follows: when 0 is present<t<0.05s, load P ═ 6 × 104×120W; when t is more than or equal to 0.05<0.1s, load P ═ 8 × 105×120W; when t is more than or equal to 0.1s, the load is the same as the first example. Get v1＝v2＝…＝v10＝2463V。
Example six: the change of the load of the direct current distribution system is the same as that of the fifth embodiment, and v is taken1＝v2＝2463V,v3＝v4L＝v10＝2455V。
Comparative example: the maximum load vector of the direct current distribution system is the same as that of the first and second embodiments, and the maximum load vector is obtained by adopting a document Simpson-Porco J W,
Figure GDA0002244709580000071
F，Bullo F.Voltage collapse in complex power grids[J].Nature communications,2016,7:10790.]the method in (1) is used for analysis, and the following analysis conclusion is obtained: when the reference voltage of the system satisfies the condition of 4| (diag { ζ } Y)1diag{ζ})-1Θ||∞When the number is less than 1, a trend feasible solution exists in the system.
The conclusion obtained by the invention can replace the conclusion obtained by calculation of a comparative example according to the sufficient condition T provided by the invention and having a feasible solution of the trend.
From iterative calculations, power flow solutions
Figure GDA0002244709580000072
This can be calculated by the following recursive calculation:
as shown in table 1, in the first example, since the system satisfies two power flow solution existence conditions, that is, ξ exists, q and h satisfy ξ ═ hq-1And 0mp ξ p f (ξ), so there is a trend feasible solution for the system after the voltage drops (v)3,v4,…,v10Down to 2455V) the system no longer meets the tidal current solution presence condition and therefore the balance point is lost.
TABLE 1 existence of tidal flow solutions of examples one to four
Figure GDA0002244709580000081
The iterative process of examples one to four is shown in FIG. 2, which is shown as a-1, a-2, a-3, and a-4, respectively. As can be seen from the graphs a-1 and a-3, when the system meets the condition of existence of the trend solution, the trend iterative algorithm provided by the invention has good convergence and faster convergence speed. In addition, as can be seen from fig. a-2 and a-4, the proposed iterative algorithm does not converge when the system does not satisfy the trend solution existence condition.
For the fifth and sixth examples, it can be known from the above theoretical analysis that when t is less than 0.1s, both the fifth and sixth examples satisfy the existence condition of the tidal current solution, so that the system has a balance point; when t is greater than 0.1s, the case five meets the existence condition of the tidal current solution, the case six does not meet the existence condition of the tidal current solution, and theoretical analysis shows that the balance point still exists in the case five and the balance point is lost in the case six. The simulation results of the fifth and sixth embodiments are shown in fig. 3b-1 and b-2, and when t >0.1, the system in the fifth embodiment still operates stably, and the load voltage of the sixth embodiment collapses.
In example one, take v1＝v2＝…＝v102463V (i.e., the presence condition obtained according to the present invention), the system has an equilibrium point, when:
4||(diag{ζ}Y1diag{ζ})-1Θ||∞＝1.26＞1 (9)
does not satisfy the conditions given in the literature cited in the comparative examples of the formula, and, at the same time, when v is1＝v2＝…＝v10The conditions proposed in the documents cited in the comparative examples can be:
Figure GDA0002244709580000082
similarly, in example three, v is taken1＝v2＝…＝v102096V (i.e. the presence condition obtained according to the invention), there is a balance point for the systemHowever, the conditions proposed in the literature cited for the comparative examples are not met:
4||(diag{ζ}Y1diag{ζ})-1Θ||∞＝1.2741＞1 (11)
at the same time, when v1＝v2＝…＝v10The conditions proposed in the documents cited in the comparative examples can be modified
Thus, the conservative conclusions are shown in table 2:
TABLE 2 conservative comparison of examples one, two and comparative examples
Figure GDA0002244709580000092
Therefore, the tide solution existence condition obtained by the invention has lower conservation.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (1)

1. A method for analyzing existence and stability of a tidal current solution of a direct current power distribution system is characterized in that the direct current power distribution system is of a mesh structure consisting of n converter nodes and m load nodes, the converter nodes are connected with the load nodes, and adjacent load nodes are electrically connected; the analysis method comprises the following steps:
s10, carrying out equivalent topology on the direct current distribution system by using a graph theory to obtain a power transmission network admittance matrix Y; according to ohm's law, get eachNode injection power transmission network current is,iL]TWherein isIs the output current of the converter node iLInjecting a current into the network for the load node;
wherein the current [ i ] of the power transmission networks,iL]TIs obtained by the following steps:
Figure FDA0002257261440000011
Figure FDA0002257261440000012
in the formula uSIs the output voltage of the converter node; u. ofLInjecting a voltage of the network for the load node;
s20, when the converter is in droop control, calculating to obtain an output voltage usExpression (c):
uS＝V*-KiS
in the formula V*＝[v1v2L vn]T，viIs the reference voltage of the converter; the equivalent physical meaning of K is virtual resistance, and the unit is ohm;
s30. based on the output voltage uSObtaining a steady-state working point expression of the direct current distribution system and a power flow equation of the direct current distribution system by the expression of the voltage-current characteristic of the constant power load;
wherein, the volt-ampere characteristic of the constant-power load is expressed by the following modes:
uiii＝-Pi,i∈{n+1,n+2,L,n+m}；
the steady-state working point of the direct-current power distribution system is obtained by the following steps:
Figure FDA0002257261440000014
Y1＝YLL-YLS(YSS+K-1)-1YSL；
the power flow equation of the direct current power distribution system is expressed as:
ULY1uL+ULβ+P＝0m
in the formula of ULIs the load voltage, P is the load power of the DC distribution system;
s40, calculating a power flow solution by adopting an iterative algorithm in combination with a sufficient condition T of feasible solution of the direct-current power distribution system;
the sufficient condition T of the feasible solution of the direct current power distribution system is represented as follows:
Figure FDA0002257261440000021
where ζ is the open circuit voltage of the DC distribution system, Y1 -1For the equivalent impedance matrix of the transmission network, χ and θ are matrices (diag { ζ } Y), respectively1diag{ζ})-1The Perron eigenvalues and corresponding eigenvectors of Θ,
Figure FDA0002257261440000022
Figure FDA0002257261440000023
a tidal current solution exists when the dc distribution system meets the following conditions:
(1) if there is one positive column vector ξ satisfying:
0m＜ξ＜f(ξ)
then there is a unique column vector x*Satisfies f (x)*)＝x*And ξ < x*＜1m；
(2) For any given system parameter V*Y and P if there is a positive vector ξ satisfying:
Figure FDA0002257261440000024
in the formula (II)
Figure FDA0002257261440000025
And is
Figure FDA0002257261440000026
Wherein:
Figure FDA0002257261440000027
Figure FDA0002257261440000028
function fij(q) is defined as follows:
Figure FDA0002257261440000029
if the DC power distribution system has a power flow solution, step S40 can be performed according to xn+1＝f(xn),x1＝1mAnd solving a power flow solution through an iterative algorithm.
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