CN109617079A - A kind of existence and method for analyzing stability of direct-flow distribution system flow solution - Google Patents
A kind of existence and method for analyzing stability of direct-flow distribution system flow solution Download PDFInfo
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- CN109617079A CN109617079A CN201811549770.6A CN201811549770A CN109617079A CN 109617079 A CN109617079 A CN 109617079A CN 201811549770 A CN201811549770 A CN 201811549770A CN 109617079 A CN109617079 A CN 109617079A
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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
- H02J3/04—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
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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
- 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]
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Abstract
The technical field of operation power of the present invention, more particularly, to the existence and method for analyzing stability of a kind of direct-flow distribution system flow solution, comprising: equivalent topologies are carried out to direct-flow distribution system and obtain power transmission network admittance matrix Y；Obtain the electric current of each node injection power transmission network；When converter is in sagging control, output voltage u is calculateds；Based on output voltage uSExpression formula and constant power load C-V characteristic, obtain the power flow equation of direct-flow distribution system steady operation point expression formula and direct-flow distribution system；In conjunction with the feasible sufficient conditions for solution T of direct-flow distribution system, flow solution is calculated using iterative algorithm.The present invention is based on the system existence consition of numeric type, can after rapid evaluation load access and voltage jump system flow solution existence, know the operating status of direct-flow distribution system；And the present invention takes full advantage of the self-characteristic of circuit system, proposes the method based on nested interal theorem, obtains the lower flow solution existence consition of conservative.
Description
Technical field
The present invention relates to the technical fields of operation power, more particularly, to a kind of depositing for direct-flow distribution system flow solution
In property and method for analyzing stability.
Background technique
With the DC loads specific gravity such as the once-through types such as photovoltaic, energy-storage battery power supply and electric car, data service station
Increase, the application demand of direct-flow distribution system will be increasing.Currently, the country is concentrated mainly on exchange to the research of power distribution network and matches
Power grid compares AC distribution net, and DC distribution net has the advantage that conversion links are few, and transition loss rate is low and high reliablity；
There is no idle, efficiency of transmission height；There is no Frequency Synchronization problems, it is easier to which renewable energy is grid-connected and the stabilization of system
Property.Therefore, direct-flow distribution system is more and more widely used.
In direct-flow distribution system, load is generally connected by a DC/DC DC/AC converter with DC bus.
When the response of load end converter is very fast, negative resistance character is presented in entire load, can be equivalent to constant power load.In order to protect
The reliable and stable operation of direct-flow distribution system energy is demonstrate,proved, voltage stability is most important.Currently, the stability about direct-flow distribution system
Research has focused largely on the small-signal stability of system, i.e. stability near operating point, and proposes corresponding stabilize and control
System strategy.However, when direct-flow distribution system is larger, the more and line impedance of load is higher, due to line loss
Reason, with the increase of load, system may lost equalization point, so as to cause voltage collapsing, is unable to control using the above method
Voltage stability.
Summary of the invention
It is an object of the invention to overcome the deficiencies of the prior art and provide direct-flow distribution systems under a kind of sagging control model
The existence and method for analyzing stability of flow solution obtain the low flow solution existence consition of conservative, rapidly assessment load
The power flow feasible solution existence of system after access and voltage jump.
In order to solve the above technical problems, the technical solution adopted by the present invention is that:
The existence and method for analyzing stability of a kind of direct-flow distribution system flow solution are provided, the direct-flow distribution system is
The reticular structure being made of n converter node and m load node, the converter node is connect with load node, adjacent
Load node electrical connection；The analysis method the following steps are included:
S10. Graph Theory is utilized, equivalent topologies are carried out to the direct-flow distribution system and obtain power transmission network admittance matrix Y；
According to Ohm's law, the electric current [i of each node injection power transmission network is obtaineds,iL]T, wherein isFor the output electricity of converter node
Stream, iLFor the electric current of load node injection network；
S20. it when converter is in sagging control, calculates and obtains output voltage usExpression formula；
S30. it is based on output voltage uSExpression formula and constant power load C-V characteristic, obtain direct-flow distribution system stable state
The power flow equation of operating point expression formula and direct-flow distribution system；
S40. the feasible sufficient conditions for solution T of direct-flow distribution system is combined, flow solution is calculated using iterative algorithm.
The existence and method for analyzing stability of direct-flow distribution system flow solution of the invention, under sagging control model into
Row, including direct-flow distribution system tidal current mathematical model is established, obtaining system by nested interal theorem, there are power flow feasible solutions
Adequate condition.Reference voltage matrix, maximum load parameter matrix, line parameter circuit value matrix are substituted into adequate condition, determine trend
Feasible solution existence.Analysis method of the invention can the flow solution to large-scale complex network quickly calculated, avoid rule
The non-linear continuous tide Solve problems of mould, to system structure without particular requirement, applied widely, calculating process simplifies, can
Effectively analyze the stability of complicated direct-current grid；And the present invention rapidly assesses load access by iterative algorithm and voltage is prominent
The flow solution existence of system, can reduce existence consition and conservative after change, being capable of the more accurately computational load upper limit.
Preferably, in step S10, the electric current [i of power transmission networks,iL]TIt is obtained by following manner:
In formula, uSFor the output voltage of converter node；uLFor the voltage of load node injection network.
Preferably, in step S20, output voltage uSIt is obtained by following manner:
uS=V*-KiS (2)
V in formula*=[v1 v2 … vn]T, viFor the reference voltage of converter；K is real number coefficient.
Preferably, in step S30, the C-V characteristic of constant power load is expressed by following manner:
uiii=-Pi,i∈{n+1,n+2,…,n+m} (3)
Preferably, in step S30, direct-flow distribution system steady operation point is obtained by following manner:
Preferably, in step S30, the power flow equation of direct-flow distribution system is indicated are as follows:
ULY1uL+ULβ+P=0m (5)
In formula, ULFor load voltage, P is the bearing power of direct-flow distribution system.
If the steady operation point expression formula of system is there are when real solution, there are equalization points for system, that is, there is feasible flow solution.
The problem of present invention research, can be described as: under the conditions of the line parameter circuit value matrix Y of system and maximum load parameter P have determined that, if
Set suitable converter reference voltage V*Guaranteeing system, there are power flow feasible solutions；In the reference voltage V of converter*And line parameter circuit value
Under the conditions of matrix Y has determined that, guaranteeing system, there are the bearing power P that under the premise of power flow feasible solution, computing system can be born
Maximum value.
Preferably, in step S40, when direct-flow distribution system meets the following conditions, there are flow solutions:
(3) a positive column vector ξ meets if it exists:
0m< ξ < f (ξ) (6)
So column vector x of existence anduniquess*Meet f (x*)=x*And ξ < x*< 1m；
(4) for any given system parameter V*, Y and P, a positive vector ξ meets if it exists:
There is solution in formula (5)AndWherein:
Q=[q1 q2 … qm]T
Function fij(q) it is defined as follows:
Preferably, if direct-flow distribution system is there are when flow solution, step S40 can be according to xn+1=f (xn),x1=1mPass through
Iterative algorithm acquires flow solution.
Preferably, in step S40, the feasible sufficient conditions for solution T of direct-flow distribution system is indicated are as follows:
Wherein, ζ is the open-circuit voltage of direct-flow distribution system, Y1 -1For the equivalent impedance matrix of power transmission network, χ and θ are respectively
Matrix (diag { ζ } Y1diag{ζ})-1The Perron characteristic value and corresponding feature vector of Θ, θ=
min{θ}。
Compared with prior art, the beneficial effects of the present invention are:
(1) present invention takes full advantage of the self-characteristic of circuit system, proposes the method based on nested interal theorem, obtains
The lower flow solution existence consition of conservative is arrived；
(2) present invention demonstrates the uniqueness of flow solution according to the property of the limit, while the iteration for giving flow solution is calculated
Method；
(3) sum that the present invention has obtained a parsing can according to analysis condition based on the system existence consition of numeric type
The rapidly power flow feasible solution existence of assessment load access and system after voltage jump；According to numeric type condition, can reduce
More accurate upper loading limit is calculated in the conservative of existence consition.
Detailed description of the invention
Fig. 1 is the equivalent topologies figure of direct-flow distribution system in embodiment two.
Fig. 2 is that the iteration of one~example of example four in embodiment two emulates schematic diagram.
Fig. 3 is the iteration emulation schematic diagram of example five in embodiment two, example six.
Specific embodiment
The present invention is further illustrated With reference to embodiment.Wherein, attached drawing only for illustration,
What is indicated is only schematic diagram, rather than pictorial diagram, should not be understood as the limitation to this patent；Reality in order to better illustrate the present invention
Example is applied, the certain components of attached drawing have omission, zoom in or out, and do not represent the size of actual product；To those skilled in the art
For, the omitting of some known structures and their instructions in the attached drawings are understandable.
Embodiment one
The existence and method for analyzing stability of a kind of direct-flow distribution system flow solution are provided, the direct-flow distribution system is
The reticular structure being made of n converter node and m load node, the converter node is connect with load node, adjacent
Load node electrical connection；The analysis method the following steps are included:
S10. Graph Theory is utilized, equivalent topologies are carried out to the direct-flow distribution system and obtain power transmission network admittance matrix Y；
According to Ohm's law, the electric current [i of each node injection power transmission network is obtaineds,iL]T, wherein isFor the output electricity of converter node
Stream, iLFor the electric current of load node injection network；
S20. it when converter is in sagging control, calculates and obtains output voltage usExpression formula；
S30. it is based on output voltage uSExpression formula and constant power load C-V characteristic, obtain direct-flow distribution system stable state
The power flow equation of operating point expression formula and direct-flow distribution system；
S40. the feasible sufficient conditions for solution T of direct-flow distribution system is combined, flow solution is calculated using iterative algorithm.
In step S10, the electric current [i of power transmission networks,iL]TIt is obtained by following manner:
In formula, uSFor the output voltage of converter node；uLFor the voltage of load node injection network.
In step S20, output voltage uSIt is obtained by following manner:
uS=V*-KiS (2)
V in formula*=[v1 v2 … vn]T, viFor the reference voltage of converter；K is real number coefficient.
In step S30, the C-V characteristic of constant power load is expressed by following manner:
uiii=-Pi,i∈{n+1,n+2,…,n+m} (3)
Direct-flow distribution system steady operation point is obtained by following manner:
The power flow equation of direct-flow distribution system indicates are as follows:
ULY1uL+ULβ+P=0m (5)
In formula, ULFor load voltage, P is the bearing power of direct-flow distribution system.
If the steady operation point expression formula of system is there are when real solution, there are equalization points for system, that is, there is feasible flow solution.
The problem of present invention research, can be described as: under the conditions of the line parameter circuit value matrix Y of system and maximum load parameter P have determined that, if
Set suitable converter reference voltage V*Guaranteeing system, there are power flow feasible solutions；In the reference voltage V of converter*And line parameter circuit value
Under the conditions of matrix Y has determined that, guaranteeing system, there are the bearing power P that under the premise of power flow feasible solution, computing system can be born
Maximum value.
In step S40, when direct-flow distribution system meets the following conditions, there are flow solutions:
(1) a positive column vector ξ meets if it exists:
0m< ξ < f (ξ) (6)
So column vector x of existence anduniquess*Meet f (x*)=x*And ξ < x*< 1m；
(2) for any given system parameter V*, Y and P, a positive vector ξ meets if it exists:
There is solution in formula (5)AndWherein:
Q=[q1 q2 … qm]T
Function fij(q) it is defined as follows:
If direct-flow distribution system is there are when flow solution, step S40 can be according to xn+1=f (xn),x1=1mIt is calculated by iteration
Method acquires flow solution.
The feasible sufficient conditions for solution T of the direct-flow distribution system of the present embodiment is indicated are as follows:
Wherein, ζ is the open-circuit voltage of direct-flow distribution system, Y1 -1For the equivalent impedance matrix of power transmission network, χ and θ are respectively
Matrix (diag { ζ } Y1diag{ζ})-1The Perron characteristic value and corresponding feature vector of Θ, θ=
min{θ}。
Embodiment two
The present embodiment is the Application Example of embodiment one, and the present embodiment has been built comprising 10 converters and 20 loads
Direct-flow distribution system, converter vertex ticks be number 1~10, load node labeled as number 11~20, converter node
The resistance sizes between resistance, load node between load node mark in Fig. 1.The present embodiment provides six examples
An and comparison example:
Example one: it is assumed that direct-flow distribution system maximum load vector is Pmax=104[10 10 10 10 10 8 8 8 8
8 10 10 10 10 10 10 12 12 12 12]TW, removing vertical coefficient is k1=k2=...=k10=2.So, work as converter
Voltage when meeting formula (7), there are power flow feasible solutions for system.Take v1=v2=...=v10=2463V.
Example two: maximum load vector is identical as example one, takes v1=v2=2463V, v3=v4...=v10=2455V.
Example three: it is assumed that direct-flow distribution system maximum load vector is Pmax=104[15 11 10 11 11 7 8 10 8
7 11 14 9 10 8 7 6 10 14 11]TW, removing vertical coefficient is k1=k2=...=k10=2.Equally, work as reference voltage
When meeting condition (7), there are power flow feasible solutions for system.Take v1=v2=...=v10=2096V.
Example four: maximum load vector is identical as example three, takes v1=v2=...=v10=2093V.
Example five: it is assumed that the variation of direct-flow distribution system load is as follows: as 0 < t < 0.05s, loading P=6 × 104×120W；
As 0.05≤t < 0.1s, P=8 × 10 are loaded5×120W；As t >=0.1s, load identical as example one.Take v1=v2=...=v10
=2463V.
Example six: the variation of direct-flow distribution system load is identical as example five, takes v1=v2=2463V, v3=v4...=v10
=2455V.
Compare example: direct-flow distribution system maximum load vector is identical as example one, example two, using document
[Simpson-Porco J W,F,Bullo F.Voltage collapse in complex power grids
[J] .Nature communications, 2016,7:10790.] method in is analyzed, and obtains analyzing conclusion as follows: when
The reference voltage of system meets condition 4 | | (diag { ζ } Y1diag{ζ})-1Θ||∞When < 1, there are power flow feasible solutions for system.
Wherein, by proposed by the present invention there are the adequate condition T of power flow feasible solution it is found that the present invention it is concluded that can
The conclusion that substitution comparison example is calculated.
According to iterative calculation, flow solutionIt can be acquired by following recursive calculation:
xk+1=f (xk),x1=120,
Calculated result is as shown in table 1, in example one, since system meets two flow solution existence consitions, that is, exists
ξ, q and h meet ξ=hq-1AndTherefore there are power flow feasible solutions for system.(the v after voltage decline3,
v4,…,v10Drop to 2455V), system no longer meets flow solution existence consition, therefore disequilibrium point.
1 example one of table arrives the existence of the flow solution of example four
Example one arrives the iterative process of example four as shown in Fig. 2, respectively as shown in a-1, a-2, a-3, a-4.By figure a-1 and
For a-3 it is found that when system meets flow solution existence consition, the trend iterative algorithm that the present invention is mentioned has good convergence
And faster convergence rate.In addition, being mentioned by figure a-2 and a-4 it is found that when system is unsatisfactory for flow solution existence consition
Iterative algorithm out is not restrained.
For example five and example six, by above-mentioned theory analysis it is found that as t < 0.1s, example five is full with example six
Sufficient flow solution existence consition, therefore system will have equalization point；As t > 0.1s, calculates column five and meet flow solution existence item
Part, example six are unsatisfactory for, and according to theory analysis it is found that example five still has equalization point, example six is by disequilibrium point.Example
Five with the simulation result of example six as shown in Fig. 3 b-1, b-2, in t > 0.1, system still stable operation in example five is calculated
The load voltage of example six collapses.
In example one, v is taken1=v2=...=v10=2463V (i.e. obtained existence consition according to the present invention) is
Just there is equalization point in system, at this time:
4||(diag{ζ}Y1diag{ζ})-1Θ||∞=1.26 > 1 (9)
It is unsatisfactory for the condition obtained in formula comparison example literature cited, meanwhile, work as v1=v2=...=v10When, comparison is calculated
The condition that example literature cited proposes can turn to:
Equally, in example three, v is taken1=v2=...=v10(obtained existence according to the present invention when=2096V
Condition), there are equalization points for system, but are unsatisfactory for the condition that comparison example literature cited proposes:
4||(diag{ζ}Y1diag{ζ})-1Θ||∞=1.2741 > 1 (11)
Meanwhile working as v1=v2=...=v10When, the condition that comparison example literature cited proposes can turn to
So conservative conclusion is as shown in table 2:
2 example one of table, example two and the conservative comparison for comparing example
As it can be seen that the obtained flow solution existence consition of the present invention has lower conservative.
Obviously, the above embodiment of the present invention be only to clearly illustrate example of the present invention, and not be pair
The restriction of embodiments of the present invention.For those of ordinary skill in the art, may be used also on the basis of the above description
To make other variations or changes in different ways.There is no necessity and possibility to exhaust all the enbodiments.It is all this
Made any modifications, equivalent replacements, and improvements etc., should be included in the claims in the present invention within the spirit and principle of invention
Protection scope within.
Claims (9)
1. a kind of existence and method for analyzing stability of direct-flow distribution system flow solution, which is characterized in that the DC distribution
System is the reticular structure being made of n converter node and m load node, and the converter node and load node connect
It connects, adjacent load node electrical connection；The analysis method the following steps are included:
S10. Graph Theory is utilized, equivalent topologies are carried out to the direct-flow distribution system and obtain power transmission network admittance matrix Y；According to
Ohm's law obtains the electric current [i of each node injection power transmission networks,iL]T, wherein isFor the output electric current of converter node, iL
For the electric current of load node injection network；
S20. it when converter is in sagging control, calculates and obtains output voltage usExpression formula；
S30. it is based on output voltage uSExpression formula and constant power load C-V characteristic, obtain direct-flow distribution system steady operation
The power flow equation of point expression formula and direct-flow distribution system；
S40. the feasible sufficient conditions for solution T of direct-flow distribution system is combined, flow solution is calculated using iterative algorithm.
2. the existence and method for analyzing stability of direct-flow distribution system flow solution according to claim 1, feature exist
In, in step S10, the electric current [i of power transmission networks,iL]TIt is obtained by following manner:
In formula, uSFor the output voltage of converter node；uLFor the voltage of load node injection network.
3. the existence and method for analyzing stability of direct-flow distribution system flow solution according to claim 2, feature exist
In, in step S20, output voltage uSIt is obtained by following manner:
uS=V*-KiS (2)
V in formula*=[v1 v2…vn]T, viFor the reference voltage of converter；K is real number coefficient.
4. the existence and method for analyzing stability of direct-flow distribution system flow solution according to claim 3, feature exist
In in step S30, the C-V characteristic of constant power load is expressed by following manner:
uiii=-Pi,i∈{n+1,n+2,…,n+m} (3)
5. the existence and method for analyzing stability of direct-flow distribution system flow solution according to claim 4, feature exist
In in step S30, direct-flow distribution system steady operation point is obtained by following manner:
6. the existence and method for analyzing stability of direct-flow distribution system flow solution according to claim 5, feature exist
In in step S30, the power flow equation of direct-flow distribution system is indicated are as follows:
ULY1uL+ULβ+P=0m (5)
In formula, ULFor load voltage, P is the bearing power of direct-flow distribution system.
7. the existence and method for analyzing stability of direct-flow distribution system flow solution according to claim 6, feature exist
In in step S40, when direct-flow distribution system meets the following conditions, there are flow solutions:
(1) a positive column vector ξ meets if it exists:
0m< ξ < f (ξ) (6)
So column vector x of existence anduniquess*Meet f (x*)=x*And ξ < x*< 1m；
(2) for any given system parameter V*, Y and P, a positive vector ξ meets if it exists:
There is solution in formula (5)AndWherein:
Function fij(q) it is defined as follows:
8. the existence and method for analyzing stability of direct-flow distribution system flow solution according to claim 7, feature exist
In if direct-flow distribution system is there are when flow solution, step S40 can be according to xn+1=f (xn),x1=1mIt is acquired by iterative algorithm
Flow solution.
9. the existence and method for analyzing stability of direct-flow distribution system flow solution according to any one of claims 1 to 8,
It is characterized in that, the feasible sufficient conditions for solution T of direct-flow distribution system is indicated in step S40 are as follows:
Wherein, ζ is the open-circuit voltage of direct-flow distribution system,For the equivalent impedance matrix of power transmission network, χ and θ are respectively matrix
(diag{ζ}Y1diag{ζ})-1The Perron characteristic value and corresponding feature vector of Θ, θ=min
{θ}。
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