CN106356859B - A kind of rectangular coordinate Newton load flow calculation method based on Matlab - Google Patents
A kind of rectangular coordinate Newton load flow calculation method based on Matlab Download PDFInfo
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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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Abstract
The invention discloses a kind of rectangular coordinate Newton load flow calculation methods based on Matlab, using matrix operation and complex operation.And Jacobian matrix and calculate node power are formed according to the programming feature of Matlab, comprising the following steps: calculate Jacobi's initial calculation matrix；Calculate node complex power and Injection Current phasor；Calculate initial Jacobian matrix piecemeal submatrix；Jacobian matrix submatrix diagonal element is corrected to voltage local derviation with node Injection Current phasor and voltage deviation；Jacobian matrix is formed by Jacobian matrix submatrix and is adjusted.The present invention is realized in Matlab platform, uses the Matlab various tools provided and function test and analysis result convenient for scientific research personnel.Program is write, modify and is debugged it was verified that the present invention had both facilitated scientific research personnel, while calculating speed provides an outstanding analysis tool also substantially close to the speed realized on C language platform for scientific research personnel.
Description
Technical field
The present invention relates to a kind of electric system Newton load flow calculation method, what especially a kind of suitable research purpose used
Rectangular coordinate Newton load flow calculation method.
Background technique
It is a basic calculating for studying power system mesomeric state operation that electric power system tide, which calculates, it is according to given operation
Condition and network structure determine the operating status of whole network.Load flow calculation is also the basis of other analyses of electric system, is such as pacified
Complete analysis, transient stability analysis etc. will use Load flow calculation.Rectangular coordinate Newton load flow calculation method is a kind of the most frequently used
Tidal current computing method, scientific research personnel often by rectangular co-ordinate Newton Power Flow calculating based on further studied.It is real
Business software is using advanced techniques such as sparse matrix technology and node optimizing codes.Although these technologies can increase substantially
The speed of Load flow calculation reduces EMS memory occupation amount, but programs very troublesome and be difficult to modify and safeguard, is not easy to increase new function
Can, thus be not suitable for scientific research personnel and use for research purposes.
Matlab software, for most basic data unit, handles various matrixes and vector operation with matrix in which can be convenient,
Complex data type can also be easily handled naturally, and common form is very close to there are also a large amount of in instruction expression formula and mathematics
Common practical function, brings convenience to programming.Matlab software is easy to use, code is short and small easy to operate, is easily programmed
And debugging, computing function is powerful, while being scientific research also with very powerful visualized graphs processing and Interactive function
And engineer application provides a kind of efficient programming tool, has become the basic tool and first choice of many scientific domains at present
Platform is widely used in various science and engineering calculation field.In order to adapt to more and more scientific research personnel's needs
The demand further studied based on being calculated on Matlab platform by rectangular co-ordinate Newton Power Flow, there is an urgent need to one
The rectangular coordinate Newton load flow calculation method that is easily programmed, modifies and debugs of the kind based on Matlab software.
Electric system node is divided into 3 classes: node active power and nothing by the characteristics of according to electric system node, Load flow calculation
The node that function power is known, node voltage amplitude and voltage phase angle are unknown is known as PQ node；Node active power and voltage magnitude
Known, node reactive power and the unknown node of voltage phase angle are known as PV node；Node voltage amplitude and voltage phase angle are it is known that section
Point active power and the unknown node of reactive power are known as balance nodes.
Newton Power Flow calculating is divided into two classes: Newton Power Flow calculates interior joint voltage using polar coordinates
Calculation method when expression, referred to as polar coordinates Newton load flow calculation method；Newton Power Flow calculates interior joint voltage using straight
Angular coordinateCalculation method when expression, referred to as rectangular coordinate Newton load flow calculation method.Rectangular co-ordinate newton
The main equation of method Load flow calculation is as follows:
Node admittance matrix are as follows:
In formula, YikIt is the transadmittance of node i and node k, as subscript i as subscript i ≠ k for node admittance matrix element
It is the self-admittance of node i when=k；N is number of nodes.
Node power equation are as follows:
In formula, Pi、QiThe respectively node active power and reactive power of node i；ei、ekRespectively node i and node k
Node voltage phasor real part；fiAnd fkThe respectively node voltage phasor imaginary part of node i and node k；Gik、BikRespectively node
Admittance matrix element YikReal and imaginary parts.
Power deviation and voltage deviation equation are as follows:
In formula, Δ Pi、ΔQiThe respectively node active power deviation and reactive power deviation of node i；ΔUi 2For node i
Node voltage amplitude deviation；PiS、QiSRespectively node i given node injection active power and injection reactive power；UiSFor
The given node voltage amplitude of node i；M is PQ number of nodes.
Power deviation and voltage deviation equation can also indicate are as follows:
In formula, ai、biThe respectively real and imaginary parts of the Injection Current phasor of node i are
Update equation group are as follows:
In formula, J is Jacobian matrix, and H, N, M, L, R, K are the piecemeal submatrix of Jacobian matrix.Each member of Jacobian matrix
Plain calculation formula are as follows:
As j ≠ i
Hij=-Gijei-Bijfi (7)
Nij=Bijei-Gijfi (8)
Mij=Bijei-Gijfi (9)
Lij=Gijei+Bijfi (10)
Rij=0 (11)
Kij=0 (12)
As j=i
Hii=-Giiei-Biifi-ai (13)
Nii=Biiei-Giifi-bi (14)
Mii=Biiei-Giifi+bi (15)
Lii=Giiei+Biifi-ai (16)
Rii=-2ei (17)
Kii=-2fi (18)
As shown in Figs. 1-2, existing rectangular coordinate Newton load flow calculation method, mainly comprises the steps that
A, initial data input and voltage initialization；
Initial data includes line and transformer branch data, node injection active power and reactive power, node voltage
Amplitude, node reactive compensation data and convergence precision, maximum number of iterations.
Voltage initialization draws definite value, PQ node using flat starting, i.e. the node voltage real part of PV node and balance nodes
Node voltage real part take 1.0；The imaginary part of all node voltages all takes 0.0.Here unit uses per unit value.
B, node admittance matrix is formed；
The node admittance matrix as shown in formula (1) is formed according to the line and transformer branch data of input.
C, Jacobian matrix is formed；
The each element of Jacobian matrix is calculated by formula (7)~formula (18) and formula (5).
D, calculate node power and power deviation and voltage deviation；
By formula (2) calculate node power, by formula (3) calculate node power deviation and node voltage deviation.
E, solve equation and correct node voltage real part e and imaginary part f；
It solves update equation group (6), finds out voltage real part correction amount column vector Δ e and voltage imaginary part correction amount column vector Δ f.
Voltage correction formula are as follows:
In formula, subscript (t) indicates the value of the t times iteration；ΔeiWith Δ fiThe respectively node voltage real part amendment of node i
Amount and node voltage imaginary part correction amount.
F, judge maximum amount of unbalance | Δ P |max、|ΔQ|maxWith | Δ U2|maxWhether convergence precision ε is both less than；If all
Less than convergence precision ε, step G is carried out, otherwise return step C carries out next iteration；
G, the active power and reactive power of calculated equilibrium node and the reactive power of PV node calculate each branch wattful power
Rate and reactive power terminate.
It is slower to directly adopt the rectangular co-ordinate Newton Power Flow software for calculation calculating speed that above-mentioned principle is realized, commercially uses
Rectangular co-ordinate Newton Power Flow software for calculation use sparse matrix technology and node optimizing code technology, it is more complicated, it is uncomfortable
Close scientific research personnel's further progress scientific research based on this.Therefore, Chinese patent ZL201010509556.5 proposes one
The Newton load flow calculation method that the suitable research purpose of kind uses, to be carried out based on the calculating of polar coordinates Newton Power Flow into one
The scientific research personnel of step research provides the Newton load flow calculation method for being easy to modify and safeguard, its characteristics are as follows:
(1) sparse matrix technology and node optimizing code are not used, the realization difficulty of algorithm is greatly reduced；
(2) unnecessary operation is avoided by simple logic judgement, improves the calculating speed of Load flow calculation.
Chinese patent ZL201010509556.5 proposed method is to be carried out based on the calculating of polar coordinates Newton Power Flow
The scientific research personnel further studied provides the polar coordinates Newton load flow calculation method for being easy to modify and safeguard.This method
Quickly using speed when the realization of the compiled programming languages such as C language, when but being realized using this kind of explanation type programming language of Matlab
The characteristics of calculating speed is then very slow, while the patent does not make full use of Matlab to be good at matrix operation and complex operation yet.Cause
This needs make full use of Matlab the characteristics of and calculates quick rectangular coordinate Newton load flow calculation method to supply
The scientific research personnel that scientific research is carried out on Matlab platform uses.
Summary of the invention
To solve the above problems existing in the prior art, the present invention will propose a kind of rectangular co-ordinate newton based on Matlab
Method tidal current computing method can make full use of Matlab distinctive the characteristics of being good at matrix operation and complex operation, while have again
The rectangular coordinate Newton load flow calculation method of very fast calculating speed.
To achieve the goals above, technical scheme is as follows: a kind of rectangular co-ordinate Newton method based on Matlab
Tidal current computing method, using matrix operation and complex operation.The following steps are included:
A, initial data input and voltage initialization；
B, node admittance matrix is formed；
C, Jacobian matrix and calculate node power are formed；
Matlab is good at matrix operation and complex operation, therefore is programmed using Matlab, it should derive and be transported based on matrix
Calculate the Jacobian matrix calculation method with complex operation.
Jacobian matrix element is related with node type, and routine will judge node type when forming Jacobian matrix, according to
Node type determines which node needs to form Jacobian matrix element.The algorithm for realizing by recycling is handled in this way,
It is easily processed, but does not fit through the method that matrix integral operation forms Jacobian matrix.Therefore, the present invention forms Jacobean matrix
When battle array, does not judge node type, Jacobian matrix element is all formed to all nodes, removes unwanted row and column again later.
The formula that Jacobian matrix element and node power are calculated using matrix operation is derived below.
To the analysis of formula (7)~formula (10), can obtain
Mij=Nij (21)
Lij=-Hij (22)
Therefore, H is first soughtijAnd Nij, find out HijAnd NijAfterwards, natural to obtain MijAnd Lij。
Before deriving the formula for calculating Jacobian matrix by matrix operation, first look at Jacobian matrix each element how with again
Several or phasor representation.
From formula (7) and formula (8) as it can be seen that Jacobian matrix each element should be by YijWithConjugationProduct, i.e.,
It obtains.Therefore Hij、Nij、Mij、LijIt can be generated by following formula:
In formula, subscript (^) indicates the conjugation of plural number.
Formula (23) can regard the matrix J obtained by node admittance matrix and following formula corresponding position element multiplication as0The i-th row
The element of jth column:
Formula (24) then can be used a matrix fill-in function repmat of Matlab to realize, therefore the sub- square of Jacobian matrix piecemeal
Battle array can be obtained by following formula:
In formula, J0For Jacobi's initial calculation matrix；Repmat is the matrix fill-in function of Matlab, 1 expression in function
When fillingRow be repeated 1 times, in function n indicate filling whenColumn repeat n times；.* indicate that two matrixes correspond to the element of ranks
It is multiplied.
By J0Obtain initial Jacobian matrix piecemeal submatrix are as follows:
H0=-Re (J0) (26)
N0=Im (J0) (27)
M0=Im (J0) (28)
L0=Re (J0) (29)
In formula, H0、N0、M0、L0For the piecemeal submatrix of initial Jacobian matrix；Re indicates to take the real part of matrix element；Im
Expression takes the imaginary part of matrix element.
The nondiagonal element of the initial Jacobian matrix piecemeal submatrix obtained by formula (26)~formula (29) has been Jacobi
Matrix element, diagonal element also need to correct.
The the 1st and the 2nd in formula (13)~formula (16) on the right side of equation is exactly H0、N0、M0、L0Diagonal element, therefore only need pair
Obtained H0、N0、M0、L0Use aiAnd biAmendment, can obtain Jacobian matrix piecemeal submatrix diagonal element.
The control variable summed in node power equation (2) is changed into j, and is rearranged are as follows:
Formula (23) expansion are as follows:
Observation type (30) and formula (31), can obtain complex power:
In formula,For complex power column vector.
Injection Current phasor are as follows:
In formula,For Injection Current phasor column vector；For node voltage column vector.
Due to ai、biThe respectively real and imaginary parts of the Injection Current phasor of node i, therefore
In formula,For the Injection Current phasor of node i.
Jacobian matrix piecemeal submatrix diagonal element is modified with Injection Current phasor as follows:
Voltage deviation is 0 to the nondiagonal element of voltage local derviation, diagonal element are as follows:
Rii=-2eiI=m+1 ..., n-1 (40)
Kii=-2fiI=m+1 ..., n-1 (41)
The element of R, K m+1 row to n-1 row can be put into the correspondence row of M, L, form M ', L ':
Mi′j=MijI=1 ..., m j=1 ..., n-1 (42)
Li′j=LijI=1 ..., m j=1 ..., n-1 (43)
Mi′j=RijI=m+1 ..., n-1 j=1 ..., n-1 (44)
Li′j=KijI=m+1 ..., n-1 j=1 ..., n-1 (45)
Form Jacobian matrix and calculate node power, comprising the following steps:
C1, Jacobi's initial calculation matrix J is calculated0；
C2, calculate node complex power；
C3, by J0Calculate initial Jacobian matrix piecemeal submatrix；
C4, Injection Current phasor is calculated；
C5, Jacobian matrix piecemeal submatrix diagonal element is modified with Injection Current phasor；
C6, R, K are calculated, forms M ', L '；
C7, Jacobian matrix is formed by Jacobian matrix piecemeal submatrix；
C8, Jacobian matrix is adjusted, removes balance nodes active power deviation and reactive power deviation is corresponding
Row；Remove balance nodes voltage real part correction amount and the corresponding column of voltage imaginary part correction amount, terminates.
D, calculate node power deviation and node voltage deviation；
Formula (4) calculate node power deviation and voltage deviation equation are write as the formation of matrix operation are as follows:
In formula, Δ P, Δ Q are respectively node active power deviation column vector and reactive power deviation column vector；ΔU2For section
Point voltage magnitude deviation column vector；PS、QSRespectively the given injection active power column vector of node and injection reactive power arrange to
Amount；USFor node voltage given value column vector；For node voltage column vector.
Remove PV node reactive power deviation and balance nodes in node power the bias vector Δ P and Δ Q being calculated
Active power deviation and reactive power deviation；Node voltage amplitude deviation column vector removes the node electricity of PQ node and balance nodes
Pressure amplitude value deviation.
E, solve equation and correct voltage real part e and imaginary part f；
The solution system of linear equations algorithm solution update equation group (6) for calling directly Matlab software, finds out node voltage real part
Correction amount column vector Δ e and node voltage imaginary part correction amount column vector Δ f.
The formula (19) and formula (20) being modified to voltage are rewritten into matrix form are as follows:
e(t+1)=e(t)-Δe(t) (48)
f(t+1)=f(t)-Δf(t) (49)
In formula, subscript (t) indicates the value of the t times iteration；Δ e and Δ f is respectively node voltage real part correction amount column vector
With node voltage imaginary part correction amount column vector.
F, judge maximum amount of unbalance | Δ P |max、|ΔQ|maxWith | Δ U2|maxWhether convergence precision ε is both less than；If all
Less than convergence precision ε, step G is carried out, otherwise return step C carries out next iteration.
G, the active power and reactive power of calculated equilibrium node and the reactive power of PV node calculate each branch wattful power
Rate and reactive power terminate.
Compared with prior art, the invention has the following advantages:
1, method proposed by the present invention is realized in Matlab platform, the various works for using Matlab to provide convenient for scientific research personnel
Tool and function are tested and are analyzed to calculated result.
2, method proposed by the present invention uses matrix operation and complex operation, reduces program code, simplifies programming, make
Calling program is more clear, and is modified program convenient for scientific research personnel, is debugged and improve to program, adds new function.
3, optimize since Matlab carries out matrix operation, using matrix operation than being programmed by matrix element loop computation
Faster, while the equation solution algorithm of Matlab is called directly, also substantially increases calculating speed.It was verified that of the invention
Method both facilitated scientific research personnel program write, modify and is debugged, while calculating speed is also substantially close in C language
The speed realized on speech platform, provides an outstanding analysis tool for the research work of scientific research personnel.
Detailed description of the invention
The present invention shares attached drawing 4 and opens.Wherein:
Fig. 1 is the flow chart that existing rectangular co-ordinate Newton Power Flow calculates.
Fig. 2 is the flow chart that existing rectangular co-ordinate Newton method forms Jacobian matrix.
Fig. 3 is the flow chart that rectangular co-ordinate Newton Power Flow of the present invention calculates.
Fig. 4 is the flow chart that the present invention forms Jacobian matrix and calculate node power.
Specific embodiment
The present invention is described further with reference to the accompanying drawing, it is modified to one according to process shown in Fig. 3-4
445 node real system examples are calculated.
The practical large-scale power system of 445 nodes has 445 nodes, and 544 branches contain a large amount of small impedance branches.For
Various methods are compared, these small impedance branches are changed to normal impedance branch to meet the requirement of various methods.
445 node real system examples are calculated using the present invention and several control methods, convergence essence when calculating
Degree is 0.00001.Several Load flow calculation algorithms are respectively as follows:
Method 1: Chinese patent ZL201010509556.5 method is changed to Cartesian form, real using Matlab language
It is existing.
Method 2: Chinese patent ZL201010509556.5 method is changed to Cartesian form, real using Matlab language
It is existing, but solve equation the equation solving algorithm for calling directly Matlab.
Method 3: Chinese patent ZL201010509556.5 method is changed to Cartesian form, real using Matlab language
It is existing, but the equation solving algorithm for calling directly Matlab is solved equation, while to the predefined dimension of matrix variables.
Method 4: the method for the present invention.
The calculating time of several method is shown in Table 1, and calculating the time does not include that data reading and output and branch power calculate
Time.
Several rectangular co-ordinate Newton Power Flows of the table 1 calculating calculating time compares
| Tidal current computing method | It calculates time (s) |
| Method 1 | 20.167 |
| Method 2 | 4.730 |
| Method 3 | 1.027 |
| Method 4 | 0.562 |
As seen from Table 1, Chinese patent ZL201010509556.5 method is changed to directly adopt when Cartesian form
Matlab is realized, it is very long to calculate the time；Patent ZL201010509556.5 method is changed to Cartesian form and directlys adopt
When Matlab is realized, if calling directly the method that solves equation of Matlab, calculating speed can be greatly improved, the solution side of Matlab
Cheng Fangfa comparative maturity is stablized, and algorithm stability is conducive to, and the calling for solving equation method of Matlab is also very simple, simplifies
Programming, is more clear program；If avoiding program from constantly expanding in the process of implementation the predefined dimension of matrix variables simultaneously
The size of matrix can greatly improve calculating speed.Using matrix when calculated result of the invention shows to be formed Jacobian matrix
Computing further can greatly improve calculating speed, and program is also further simplified.
The method of the present invention can be realized in the MATLAB programming language of any version, but be suggested using more recent version
MATLAB language.
The present invention is not limited to the present embodiment, any equivalent concepts within the technical scope of the present disclosure or changes
Become, is classified as protection scope of the present invention.
Claims (1)
1. a kind of rectangular coordinate Newton load flow calculation method based on Matlab, comprising the following steps:
A, initial data input and voltage initialization；
Initial data include line and transformer branch data, node injection active power and reactive power, node voltage amplitude,
Node reactive compensation data and convergence precision and maximum number of iterations；
Voltage initialization draws definite value, the section of PQ node using flat starting, i.e. the node voltage real part of PV node and balance nodes
Point voltage real part takes 1.0；The imaginary part of all node voltages all takes 0.0；Here unit uses per unit value；
The PQ node is the node that active power and reactive power are known, voltage magnitude and voltage phase angle are unknown, described
PV node is active power and the node that voltage magnitude is known, reactive power and voltage phase angle are unknown, and the balance nodes are
Voltage magnitude and voltage phase angle are it is known that the unknown node of the active power and reactive power of node；
B, node admittance matrix is formed；
The node admittance matrix as shown in formula (1) is formed according to the line and transformer branch data of input；
In formula, YikIt is the transadmittance of node i and node k, as subscript i=k as subscript i ≠ k for node admittance matrix element
When, it is the self-admittance of node i；N is number of nodes；
It is characterized in that, further comprising the steps of:
C, Jacobian matrix and calculate node power are formed；
C1, Jacobi's initial calculation matrix J is calculated0；
In formula, J0For Jacobi's initial calculation matrix；For the column vector of node voltage conjugation；Repmat is the matrix of Matlab
Stuffing function, 1 when indicating filling in functionRow be repeated 1 times, in function n indicate filling whenColumn repeat n times；.* it indicates
Two matrixes correspond to the element multiplication of ranks；
C2, calculate node complex power；
The node complex power column vector being made of each node complex power are as follows:
In formula,For node complex power column vector；Subscript ^ indicates the conjugation of plural number；
C3, initial Jacobian matrix piecemeal submatrix is calculated by J0；
By J0Obtain initial Jacobian matrix piecemeal submatrix are as follows:
H0=-Re (J0) (4)
N0=Im (J0) (5)
M0=Im (J0) (6)
L0=Re (J0) (7)
In formula, H0、N0、M0、L0For the piecemeal submatrix of initial Jacobian matrix；Re indicates to take the real part of matrix element；Im is indicated
Take the imaginary part of matrix element；
C4, Injection Current phasor is calculated；
In formula,For Injection Current phasor column vector；
C5, initial Jacobian matrix piecemeal submatrix diagonal element is modified with Injection Current phasor it is as follows:
In formula,For the Injection Current phasor of node i；M is PQ number of nodes；
C6, R, K are calculated, forms M ', L '；
Voltage deviation is 0 to the nondiagonal element of voltage local derviation, diagonal element are as follows:
Rii=-2eiI=m+1 ..., n-1 (13)
Kii=-2fiI=m+1 ..., n-1 (14)
With the correspondence row of the element replacement M of R m+1 row to n-1 row, M ' is formed；L is replaced with the element of K m+1 row to n-1 row
Correspondence row, formed L '；
C7, Jacobian matrix is formed by revised Jacobian matrix piecemeal submatrix；
In formula, J is Jacobian matrix, H, N, M ', the piecemeal submatrix that L ' is revised Jacobian matrix；
C8, Jacobian matrix is adjusted, removes balance nodes active power deviation and the corresponding row of reactive power deviation；It goes
Fall balance nodes voltage real part correction amount and the corresponding column of voltage imaginary part correction amount, terminates；
D, calculate node power deviation and node voltage deviation；
Node power deviation and node voltage deviation is calculated as follows:
In formula, Δ P, Δ Q are respectively node active power deviation column vector and reactive power deviation column vector；ΔU2For node electricity
Pressure amplitude value deviation column vector；PS、QSRespectively given node injection active power column vector and injection reactive power column vector；
USFor node voltage given value column vector；For node voltage column vector；
Remove PV node reactive power deviation in node power the bias vector Δ P and Δ Q being calculated and balance nodes are active
Power deviation and reactive power deviation；Node voltage amplitude deviation column vector removes the node voltage width of PQ node and balance nodes
It is worth deviation；
E, solve equation and correct voltage real part e and imaginary part f；
Obtain that Jacobian matrix J and step D obtains node power bias vector Δ P and Δ Q and node voltage amplitude is inclined by step C
Difference vector Δ U2, the update equation for being configured to Load flow calculation is as follows:
The solution system of linear equations algorithm solution update equation group (17) for calling directly Matlab software, find out voltage real part correction amount to
Measure Δ e and voltage imaginary part correction amount vector Δ f；
Node voltage real and imaginary parts are modified as the following formula:
e(t+1)=e(t)-Δe(t) (18)
f(t+1)=f(t)-Δf(t) (19)
In formula, subscript (t) indicates the value of the t times iteration；
F, judge maximum amount of unbalance | Δ P |max、|ΔQ|maxWith | Δ U2|maxWhether convergence precision ε is both less than；If both less than
Convergence precision ε carries out step G, and otherwise return step C carries out next iteration；
G, the active power and reactive power of calculated equilibrium node and the reactive power of PV node, calculate each branch active power and
Reactive power terminates.
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| CN110336288B (en) * | 2019-07-30 | 2022-08-16 | 大连海事大学 | Three-phase power flow calculation method for power distribution network based on extraction of Jacobian elements through matrix operation |
| CN110336287B (en) * | 2019-07-30 | 2022-08-12 | 大连海事大学 | Three-phase load flow calculation method of power distribution system based on Jacobian element extraction |
| CN113158126B (en) * | 2021-04-27 | 2023-05-05 | 广西大学 | Calculation method for extracting complex power equation hessian matrix of polar coordinate node |
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| CN101621200A (en) * | 2009-08-04 | 2010-01-06 | 大连海事大学 | Rectangular coordinate Newton load flow calculation method |
| CN101976838A (en) * | 2010-10-15 | 2011-02-16 | 大连海事大学 | Newton-process power flow calculation method for study purpose |
| CN103441496A (en) * | 2013-09-04 | 2013-12-11 | 博爱县电业公司 | MATLAB-based electric-power-system load-flow calculation method |
| WO2014186187A1 (en) * | 2013-05-14 | 2014-11-20 | Rensselaer Polytechnic Institute | Methods of computing steady-state voltage stability margins of power systems |
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| CN101621200A (en) * | 2009-08-04 | 2010-01-06 | 大连海事大学 | Rectangular coordinate Newton load flow calculation method |
| CN101976838A (en) * | 2010-10-15 | 2011-02-16 | 大连海事大学 | Newton-process power flow calculation method for study purpose |
| WO2014186187A1 (en) * | 2013-05-14 | 2014-11-20 | Rensselaer Polytechnic Institute | Methods of computing steady-state voltage stability margins of power systems |
| CN103441496A (en) * | 2013-09-04 | 2013-12-11 | 博爱县电业公司 | MATLAB-based electric-power-system load-flow calculation method |
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