CN110148946A - A kind of isolated island micro-capacitance sensor tidal current computing method solved based on two step of confactor - Google Patents
A kind of isolated island micro-capacitance sensor tidal current computing method solved based on two step of confactor Download PDFInfo
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Classifications
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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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- H02J3/382—
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- H02J3/383—
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- H02J3/386—
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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
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/388—Islanding, i.e. disconnection of local power supply from the network
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/50—Photovoltaic [PV] energy
- Y02E10/56—Power conversion systems, e.g. maximum power point trackers
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/70—Wind energy
- Y02E10/76—Power conversion electric or electronic aspects
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Abstract
The invention discloses a kind of isolated island micro-capacitance sensor tidal current computing methods solved based on two step of confactor, this method comprises the following steps: rewriting to former power flow equation, all constant terms are moved on on the right side of equation, and retain PV node voltage magnitude, voltage term is replaced with system frequency ω by logarithmic form;Introduce confactor y, u, by Load flow calculation it is equations turned be relation function between one group of underdetermined equation, one group of overdetermined equation and one group of confactor, set trend initial value, the equation after above-mentioned conversion is solved by two-step method, wherein the first step by it is transformed it is equations turned find for least square problem closer to the linearisation point that really solves, improve algorithm to the robustness of initial value, second step solves following iteration step variable directly to reduce calculation amount.Method of the invention can effectively improve convergence and robustness.
Description
Technical field
The present invention relates to technical field of power systems more particularly to isolated island micro-capacitance sensor Load flow calculation fields, propose one kind
The isolated island micro-capacitance sensor tidal current computing method solved based on two step of confactor.
Background technique
Micro-capacitance sensor Load flow calculation is an important field of research as micro-capacitance sensor stability analysis, the basis distributed rationally.
In micro-grid connection operation, Load flow calculation is similar to distribution power system load flow calculation.And the micro-capacitance sensor of isolated operation is controlled in equity
Under system, balance nodes are not present in system, and there are the DG of sagging control, need to solve to system frequency, therefore traditional tide
Flow calculation methodologies are no longer applicable in, and need to study the algorithm for being more suitable for isolated island micro-capacitance sensor Load flow calculation.
From the point of view of current isolated island micro-capacitance sensor Load flow calculation result of study, Part Methods are using the thought of optimization to trend side
Cheng Jinhang is solved, such as BFGS Trust Region Algorithm, Levenberg-Marquardt (LM) algorithm, but such algorithm has ginseng
Number is excessive, the problem for adjusting ginseng complicated, and there are tail portion effects for LM algorithm, it is difficult to adapt to the calculating of high-precision requirement.Another kind is thought
Road is former Power Flow Problem to be decomposed into traditional Load flow calculation and sagging node updates two sub-problems, but convergence rate is slower.For
This, it is necessary to propose a kind of isolated island micro-capacitance sensor tidal current computing method solved based on two step of confactor, it is auxiliary by introducing two
Help the factor, by former non-linear power flow equation be decomposed into one group owe constant linear equation, one group of determined linear equation and one group of auxiliary to
Relation function between amount is iterated solution to transformed equation in two steps.Through example contrast verification, which has convergence
The feature that speed is fast, strong robustness and calculating time are short.
Summary of the invention
The technical problem to be solved by the present invention is to which existing technical solution is improved and improved, one kind is provided and is based on
The isolated island micro-capacitance sensor tidal current computing method that two step of confactor solves, to improve the convergence rate and robustness that calculate.
In order to solve the above technical problems, the present invention adopts the following technical scheme:
Include the following steps:
1, Load flow calculation equation is rewritten
Two step derivation algorithm of confactor there are certain requirements the form of power flow equation, need to carry out former power flow equation
It rewrites.
Isolated island micro-capacitance sensor power flow equation can abstract representation are as follows:
The x ∈ of F (x)=0 Rn
If n node is shared in system, wherein there is nPQA PQ node, nPVA PV node and nDA sagging node, then formula (1)
Contain n+n for onePQ+nDThe n+n of a location variablePQ+nDTie up equation;
By moving on to constant terms all in above formula on the right side of equation, and retain PV node voltage magnitude, be rewritten as
Lower form:
F1(x)=p
In formula:
p0For in power flow equation constant term form vector, and be subsequent convenience of calculation, the electricity of PV node is remained in p
Pressure amplitude value indicates by its quadratic form,
For vector x, will wherein voltage term be replaced with system frequency ω by logarithmic form:
X=[δ2,…,δn,a1,…,an,w]T
In formula: δiFor node i phase angle, ai=lnVi=2lnUi, w=ln ω.
2, confactor is introduced
Confactor y, u are introduced,
In formula: item U second from the bottomD,iFor sagging node voltage amplitude, n is sharedD?;α, β are active and reactive load factor,
For the node i at each branch both ends, j enables Kij=UiUj cosδij、Lij=UiUj sinδij, wherein δij=δi-δj;
In formula: aij=ai+aj, δij=δi-δj;
By Load flow calculation it is equations turned be relationship letter between one group of underdetermined equation, one group of overdetermined equation and one group of confactor
Number, it may be assumed that
In formula: nonlinear transformation f () reversible between confactor, inverse transformation y=f-1(u) concrete form is as follows:
3, trend initial value design
Set flow state initial guess x0, the number of iterations k=0 is taken, convergence precision ε, maximum number of iterations k are setmax,
System frequency ω0, voltage magnitude U0With phase angle initial value δ0, take y0=f-1(Cx0)。
4, two-step method solves equation
The equation after above-mentioned conversion is solved by two-step method, wherein the first step will be transformed equations turned for most
Small two multiply problem to find closer to the linearisation point really solved, improve algorithm to the robustness of initial value, second step directly solves
Following iteration walks variable to reduce calculation amount.
Step 1:
1) it solves following formula and obtains vector λ:
(EET) λ=p-Eyk
2) it calculates
3)And calculate Jacobian matrix
Step 2:
1) it solves following formula and obtains xk+1:
2) y is updatedk+1=f-1(Cxk+1);
If 3) | | p-Eyk+1||∞< ε then restrains, otherwise k=k+1, and return step 1 continues iteration.
Beneficial achievement of the invention is: solving equation by the introducing of confactor and using two-step method, works as initial value
x0When deviateing farther out with the true solution of equation, classical Newton method, which is easy to appear, does not restrain or restrains slower situation.The present invention
By constructing a least square problem, finds and meet under constraint as close possible to the linearisation point really solved, can effectively mention
Better utility and robustness.
Detailed description of the invention
Fig. 1 is a kind of specific implementation example diagram of the invention: containing 115 node isolated island micro-capacitance sensor example figures.
Fig. 2 is the flow chart of the isolated island micro-capacitance sensor tidal current computing method solved the present invention is based on two step of confactor.
Fig. 3 is the present invention and Newton method (N-R), the adaptive LM algorithm (A-LM) of single step, three step LM algorithms (MTLM) not
With convergence number comparison diagram under precision.
Specific embodiment
In the following with reference to the drawings and specific embodiments, the present invention will be described in detail method and specific steps, it should be understood that these implementations
Example is only illustrative of the invention and is not intended to limit the scope of the invention, after the present invention has been read, those skilled in the art
The application range as defined in the appended claims is fallen within to the modification of various equivalent forms of the invention.
The present embodiment illustrates specific method of the present invention by taking large-scale 115 node example of micro-capacitance sensor as an example.The example has 115
Node, 118 branches contain 3 Wind turbines, 2 photovoltaic cells and 8 gas turbines, as shown in Fig. 1.
1, Load flow calculation equation is rewritten
Isolated island micro-capacitance sensor power flow equation can abstract representation are as follows:
The x ∈ of F (x)=0 Rn (12)
If n node is shared in system, wherein there is nPQA PQ node, nPVA PV node and nDA sagging node, then formula (1)
Contain n+n for onePQ+nDThe n+n of a location variablePQ+nDTie up equation.
By moving on to all constant terms in formula (1) on the right side of equation, and retain PV node voltage magnitude, formula (1) can be changed
It is written as following form:
F1(x)=p (13)
In formula:
P=[p0,V1,…,VnPV]T (14)
p0For in power flow equation constant term form vector, and be subsequent convenience of calculation, the electricity of PV node is remained in p
Pressure amplitude value indicates by its quadratic form,
For vector x, will wherein voltage term and system frequency be replaced by logarithmic form:
X=[δ2,…,δn,a1,…,an,w]T (15)
In formula: δiFor node i phase angle, ai=ln Vi=2 ln Ui, w=ln ω.
2, confactor is introduced
Introduce confactor y:
In formula: item U second from the bottomD,iFor sagging node voltage amplitude, n is sharedD?;α, β are active and reactive load factor,
For the node i at each branch both ends, j enables Kij=UiUj cosδij、Lij=UiUj sinδij, wherein δij=δi-δj。
Introduce confactor u:
In formula: item second from the bottom is identical as formula (2), represents sagging node;aij=ai+aj, δij=δi-δj。
Using confactor, former power flow equation can be become following form:
In formula: nonlinear transformation f () reversible between confactor, inverse transformation y=f-1(u) concrete form is as follows:
3, trend initial value design
Set flow state initial guess x0, the number of iterations k=0 is taken, convergence precision ε, maximum number of iterations k are setmax,
System frequency ω0, voltage magnitude U0With phase angle initial value δ0, take y0=f-1(Cx0)。
4, two-step method solves equation
After completing to the transformation of power flow equation, two-step method can be used, transformed equation is solved, specific steps are such as
Under:
Step 1:
1) it solves following formula and obtains vector λ:
(EET) λ=p-Eyk (20)
2) it calculates
3)And the Jacobian matrix of calculating formula (8)
Step 2:
1) it solves following formula and obtains xk+1:
2) y is updatedk+1=f-1(Cxk+1)。
If 3) | | p-Eyk+1||∞< ε then restrains, otherwise k=k+1, and return step 1 continues iteration.
It will be calculated in 115 node large size micro-capacitance sensors using after the method for the present invention with Newton method (N-R), the adaptive LM of single step
Method (A-LM), three step LM methods (MTLM) compare, recorded under initial value variation algorithms of different not restrain number as shown in table 1
(number of run is 100 times):
1 initial value of table changes lower 4 kinds of algorithmic statement situations comparison
It is as shown in table 2 to expend the time in 1000 Monte Carlo simulations for 4 kinds of algorithms of comparison simultaneously:
2 Monte Carlo simulation of table expends the time
Claims (5)
1. a kind of isolated island micro-capacitance sensor tidal current computing method solved based on two step of confactor, which is characterized in that including walking as follows
It is rapid:
1) Load flow calculation equation is rewritten;
2) introduce confactor, by Load flow calculation it is equations turned be one group of underdetermined equation, one group of overdetermined equation and one group of auxiliary because
Relation function between son;
3) trend initial value is set;
4) two-step method solves equation: solving to the equation after above-mentioned conversion, the first step first equations turned is by transformed
Least square problem, second step directly solve following iteration step variable.
2. the isolated island micro-capacitance sensor tidal current computing method according to claim 1 solved based on two step of confactor, feature
It is, rewriting Load flow calculation equation described in step 1), specifically: isolated island micro-capacitance sensor power flow equation can abstract representation are as follows:
The x ∈ of F (x)=0 Rn (1)
If n node is shared in system, wherein there is nPQA PQ node, nPVA PV node and nDA sagging node, then formula (1) is one
It is a to contain n+nPQ+nDThe n+n of a location variablePQ+nDTie up equation;
By moving on to all constant terms in formula (1) on the right side of equation, and retain PV node voltage magnitude, formula (1) can be rewritten as
Following form:
F1(x)=p (2)
In formula:
p0For in power flow equation constant term form vector, and be subsequent convenience of calculation, the voltage amplitude of PV node is remained in p
Value, is indicated by its quadratic form,
For vector x, will wherein voltage term be replaced with system frequency ω by logarithmic form:
X=[δ2,…,δn,a1,…,an,w]T (4)
In formula: δiFor node i phase angle, ai=lnVi=2lnUi, w=ln ω.
3. the isolated island micro-capacitance sensor tidal current computing method according to claim 2 solved based on two step of confactor, feature
It is, step 2) specifically:
Introduce confactor y:
In formula: item U second from the bottomD,iFor sagging node voltage amplitude, n is sharedD?;α, β are active and reactive load factor, for
The node i at each branch both ends, j enable Kij=UiUjcosδij、Lij=UiUjsinδij, wherein δij=δi-δj;
Introduce confactor u:
In formula: aij=ai+aj, δij=δi-δj;
Using confactor, former power flow equation can be become following form:
In formula: nonlinear transformation f () reversible between confactor, inverse transformation y=f-1(u) concrete form is as follows:
4. the isolated island micro-capacitance sensor tidal current computing method according to claim 3 solved based on two step of confactor, feature
It is, sets flow state initial guess x0, the number of iterations k=0 is taken, convergence precision ε, maximum number of iterations k are setmax, system
Frequencies omega0, voltage magnitude U0With phase angle initial value δ0, take y0=f-1(Cx0)。
5. the isolated island micro-capacitance sensor tidal current computing method according to claim 4 solved based on two step of confactor, feature
It is, after completing to the transformation of power flow equation, transformed equation is solved using two-step method, the specific steps are as follows:
Step 1:
1) it solves following formula and obtains vector λ:
(EET) λ=p-Eyk (9)
2) it calculates
3)And the Jacobian matrix of calculating formula (8)
Step 2:
1) it solves following formula and obtains xk+1:
2) y is updatedk+1=f-1(Cxk+1);
If 3) | | p-Eyk+1||∞< ε then restrains, otherwise k=k+1, and return step 1 continues iteration.
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