CN106410811B - Iteration small impedance branches endpoint changes the tidal current computing method of Jacobian matrix for the first time - Google Patents
Iteration small impedance branches endpoint changes the tidal current computing method of Jacobian matrix for the first time 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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- 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]
Abstract
The invention discloses the tidal current computing methods that a kind of iteration small impedance branches endpoint for the first time changes Jacobian matrix, and in iteration for the first time, small impedance branches endpoint is used by given value PisAnd QisCalculated aiAnd biValue calculates Jacobian matrix element, and normal leg endpoint and when subsequent each secondary iteration all nodes then use conventional method to calculate Jacobian matrix element when iteration for the first time.The present invention by iterative process for the first time small impedance branches both ends node use the Jacobian matrix calculation method different from later each secondary iterative process, solve rectangular co-ordinate Newton Power Flow and calculate convergence problem when analysis is containing small impedance branches electric system.When not restrained using the calculating of conventional Cartesian coordinate Newton Power Flow, the present invention can reliable conveyance, and it is fewer than existing patented technology the number of iterations.The present invention also can carry out Load flow calculation to normal electricity system simultaneously, without adverse effect.
Description
Technical field
The present invention relates to the tidal current computing method of the electric system containing small impedance branches, especially a kind of right angle of electric system
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 gives according to electric system
Fixed service condition and network structure determines the operating status of entire electric system.Load flow calculation is also other analyses of electric system
Basis, such as safety analysis, transient stability analysis will use Load flow calculation.Due to have convergence is reliable, calculating speed compared with
Fast and moderate memory requirements advantage, Newton method become the main stream approach of current Load flow calculation.Newton method is divided into polar coordinates and straight
The Newton Power Flow calculating of two kinds of forms of angular coordinate, two kinds of forms is all widely used in the power system.
In the calculating of rectangular co-ordinate Newton Power Flow, the voltage of node i is indicated using rectangular co-ordinate are as follows:
To normal electricity network, rectangular co-ordinate Newton Power Flow, which calculates, has good convergence, but encounters containing small resistance
When the Ill-conditioned network of anti-branch, the calculating of rectangular co-ordinate Newton Power Flow may dissipate.Electric system small impedance branches can be divided into
Small impedance line and small impedance transformer branch, in mathematical model route be considered as no-load voltage ratio be 1:1 transformer, therefore under
It is only analyzed by taking small impedance transformer branch as an example when surface analysis.Small impedance transformer model is shown in Fig. 1, the non-standard no-load voltage ratio of transformer
K is located at node i side, and impedance is located at standard no-load voltage ratio side.Transformer impedance zij=rij+jxijVery little, admittance are
In formula, yij、gij、bijAdmittance, conductance and the susceptance of small impedance branches respectively between node i and node j；rij、
xijThe resistance of small impedance branches and reactance respectively between node i and node j.
Due to small impedance branches li-jImpedance very little, the voltage drop of branch also very little, therefore the electricity of two end node of transformer
Pressure should meet:
As shown in Fig. 2, existing rectangular coordinate Newton load flow calculation method, mainly comprises the steps that
A, initial data and initialization voltage are inputted
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.
Voltage initialization draws definite value, the electricity of PQ node using flat starting, i.e. the voltage real part of PV node and balance nodes
Compacting portion takes 1.0；The imaginary part of all voltages all takes 0.0.Here unit uses per unit value.
B, node admittance matrix is formed
If node i and the original self-conductance of node j with from susceptance be respectively Gi0、Bi0、Gj0、Bj0, increase by one between them
Self-admittance and transadmittance after small impedance branches are respectively as follows:
In formula, Yii、YjjThe respectively self-admittance of node i and node j；YijFor the transadmittance between node i and node j；
rij、xijThe resistance of small impedance branches and reactance respectively between node i and node j；K small impedance between node i and node j
The no-load voltage ratio of branch (if it is power transmission line branch, no-load voltage ratio 1)；
C, power and voltage deviation are calculated
The power deviation calculation formula of PQ node are as follows:
In formula, Pis、QisRespectively node i given injection active power and reactive power, PisFor power supply active power with
The difference of load active power, QisFor the difference of power supply reactive power and reactive load power；ai、biThe respectively calculating note of node i
The real and imaginary parts for entering electric current phasor are
In formula, n is the number of nodes of electric system.
When Load flow calculation is restrained, Δ P in formula (6)i、ΔQiAll level off to 0, therefore aiAnd biEqual to by given value PisAnd Qis
Calculated aisAnd bis
The active power and voltage deviation calculation formula of PV node are as follows:
In formula, VisThe voltage magnitude given for node i.
Balance nodes are not involved in iterative calculation, do not need to calculate power deviation or voltage deviation.
Ask the value of maximum absolute value in each node power or voltage deviation, referred to as maximum amount of unbalance, if maximum uneven
The absolute value of measurement is less than given convergence precision, goes to step F, no to then follow the steps D.
D, Jacobian matrix J is formed
Element (when i ≠ j) calculation formula of Jacobian matrix J is as follows:
Element (when i=j) calculation formula of Jacobian matrix J is as follows:
PQ saves knock type (16)-(19) and calculates Jacobian matrix element；PV node is based on formula (16), (17), (20), (21)
Calculate Jacobian matrix element；Balance nodes do not calculate Jacobian matrix element.
E, update equation and amendment voltage real part e, imaginary part f are solved
The fundamental equation (6) of Load flow calculation and (9) are Nonlinear System of Equations, generally use successive Linearization Method iteration and ask
Solution.It linearizes obtained equation and is known as update equation, for seeking the correction amount of voltage real and imaginary parts.
Update equation are as follows:
In formula, J is Jacobian matrix；Δ P and Δ Q is respectively active power and reactive power deviation column vector；ΔV2For
Voltage magnitude deviation column vector；Δ e and Δ f is respectively the real and imaginary parts correction amount column vector of voltage phasor；For
For active power departure function column vector to the local derviation matrix of voltage phasor real part column vector transposition, subscript T is transposition symbol.
Voltage correction formula are as follows:
In formula, subscript t indicates the t times iteration.
F, output node and branch data.
To normal electricity network, Newton Power Flow, which calculates, has good convergence, but encounters containing small impedance branches
When Ill-conditioned network, Newton Power Flow calculating may dissipate.And small impedance branches are generally existing in electric system, convergence is electricity
The most important index of this kind of nonlinear problem of Force system Load flow calculation, calculating do not restrain that you can't get non trivial solutions.Therefore change
Kind rectangular co-ordinate Newton Power Flow is calculated to have very important significance for the convergence containing small impedance branches electric system.
Chinese patent ZL201410299531.5 discloses a kind of by modification conventional Cartesian coordinate Newton Power Flow calculating
The method of Jacobian matrix improves the convergence of Load flow calculation.Using by given value P when this method calculates Jacobi's elementis
And QisThe a of calculatingiAnd biValue efficiently solves the diverging that the small impedance branches electric power system tide for being 0 containing resistance calculates and asks
Topic.But when the resistance of small impedance branches is not 0, this method the number of iterations increases, and convergence is deteriorated, or even does not restrain.
Chinese patent ZL201410315785.1 proposes a kind of rectangular co-ordinate Newton Power Flow that Jacobian matrix changes
Calculation method, iteration and subsequent each secondary iteration use different Jacobian matrix calculation methods to this method for the first time, for the first time iteration meter
Using by given value P when calculating Jacobi's elementisAnd QisThe a of calculatingiAnd biValue, when subsequent each iterative calculation Jacobi's element still
Using conventional method, efficiently solve be not containing resistance 0 small impedance branches electric power system tide calculate divergence problem, but should
When it is not 0 small impedance branches that electric system, which includes a plurality of resistance, the number of iterations increases method, and convergence is deteriorated.
Chinese patent ZL201611094297.8 proposes a kind of ox for changing Jacobian matrix with iteration and node type
Method tidal current computing method, this method for the first time iteration when all PQ nodes with subsequent each secondary iteration using different Jacobian matrixes
Calculation method, using by given value P when all PQ nodes calculate Jacobi's element when iteration for the first timeisAnd QisThe a of calculatingiAnd bi
Value still uses tradition side when all PV nodes and when subsequent each secondary iteration all nodes calculate Jacobi's element when iteration for the first time
Method, efficiently solve electric system include a plurality of resistance be not 0 small impedance branches Load flow calculation divergence problem, but iteration
Number is still more, requires further improvement.
Summary of the invention
To solve the above problems existing in the prior art, the present invention will propose that a kind of iteration small impedance branches endpoint for the first time changes
Become the tidal current computing method of Jacobian matrix, the small impedance branches electric power that its analysis is not 0 containing resistance can be improved in this method
The convergence rate of system.
The method of traditional calculating Jacobian matrix is derived from the basic principle of Newton method, normal impedance branch
Endpoint to calculate Jacobian matrix element using conventional method be suitable, but the endpoint of small impedance branches uses conventional method meter
Calculating Jacobian matrix element then will lead to Load flow calculation diverging.For the first time when iteration, at the beginning of voltage is the voltage of flat starting method setting
Value, the injecting power for the node that the branch power that normal impedance branch calculates is not much different with actual value and these branches are connected
Calculated value and given value are close, thus for the first time the endpoint of iteration normal impedance branch calculated using injecting power calculated value it is refined can
It is also relatively more reasonable than matrix element.Small impedance branches are due to its impedance very little, the inconsistent band of both end voltage initial value and actual value
The voltage difference for the very little come will calculate very big branch power, the injecting power calculated value for the node being connected with the branch
It is very big, it will lead to Load flow calculation diverging, therefore the endpoint of iteration small impedance branches should not use injecting power calculated value for the first time
Jacobian matrix element is calculated, and injecting power given value or initial value should be used to calculate Jacobian matrix element.
To achieve the goals above, the invention proposes a kind of rectangular coordinate Newton load flow calculation methods to improve trend
Computational convergence.Small impedance branches endpoint is used by given value P when iteration for the first time of the inventionisAnd QisCalculated aiAnd biValue
Jacobian matrix element is calculated, normal leg endpoint and when subsequent each secondary iteration all nodes then use tradition when iteration for the first time
Method calculates Jacobian matrix element.
Technical scheme is as follows: iteration small impedance branches endpoint changes the Load flow calculation side of Jacobian matrix for the first time
Method, comprising the following steps:
A, initial data and initialization voltage are inputted；
B, the connected branch type T of two end nodes is determined according to the size of branch resistance and reactance
Forming node institute's chord road type array, specific step is as follows:
B1, branch data is read in, small resistance threshold r is setminWith low reactance threshold value xmin；
B2, node institute's chord road type array T are reset；
B3, m=1 is enabled；
B4, first and last node number i and j, the resistance r, reactance x for taking branch m；
B5, judge whether to meet r≤rminAnd x≤xminCondition, if conditions are not met, going to step B7；
B6, T is enabledi=1, Tj=1；
B7, m=m+1 is enabled；
B8, judge whether m is greater than circuitry number l, if m goes to step B4 no more than l；Otherwise C is gone to step；
C, node admittance matrix is formed；
D, iteration count t=0 is set；
E, power and voltage deviation are calculated, maximum amount of unbalance Δ W is soughtmax；
F, judge maximum amount of unbalance absolute value | Δ Wmax| whether it is less than convergence precision ε；If it is less than convergence precision ε, hold
Row step J；Otherwise, step G is executed；
G, Jacobian matrix is formed；
In addition to iteration for the first time, Jacobian matrix calculation method still uses conventional method.The Jacobian matrix meter of iteration for the first time
Calculation method uses distinct methods according to the type that node connects branch.For the endpoint of small impedance branches, because using tradition side
Method, which calculates Jacobian matrix, will lead to Load flow calculation diverging, so calculating injection using formula (8) when calculating Jacobian matrix element
The real and imaginary parts effect of electric current phasor is preferable；For the endpoint of normal impedance branch, Jacobi is still traditionally calculated
Matrix element, i.e., the real part a of the node i Injection Current phasor in Jacobian matrix calculation formulaiWith imaginary part biIt is calculated by formula (7).
Forming Jacobian matrix element, specific step is as follows:
G1, by formula (10)-(15) calculate i ≠ j when Jacobian matrix element；
G2, i=1 is enabled；
G3, judge whether to meet t=0 and T simultaneouslyi=1 condition, if being unsatisfactory for this condition goes to step G4；If full
Foot, then by the real part a of the Injection Current phasor of formula (8) calculate node iiWith imaginary part bi, then go to step G5；
G4, by formula (7) calculate node i Injection Current phasor real part aiWith imaginary part bi；
G5, by formula (16)-(21) calculate i=j when Jacobian matrix element；
G6, i=i+1 is enabled；
G7, judge whether i is greater than number of nodes n, if i goes to step G3 no more than n；Otherwise H is gone to step；
H, update equation and amendment voltage real part e, imaginary part f are solved；
I, t=t+1, return step E is enabled to carry out next iteration；
J, output node and branch data.
Compared with prior art, the invention has the following advantages:
1, the present invention by iterative process for the first time small impedance branches both ends node use and later each secondary iterative process
Different Jacobian matrix calculation methods solves rectangular co-ordinate Newton Power Flow and calculates and contains small impedance branches electric power in analysis
Convergence problem when system.Using conventional Cartesian coordinate Newton Power Flow calculating do not restrain when, this method can reliable conveyance,
And it is fewer than existing patented technology the number of iterations.
2, contain small impedance branch since the present invention not only can effectively solve conventional Cartesian coordinate Newton Power Flow and calculate to analyze
The convergence problem of road electric system, while can also Load flow calculation be carried out to normal electricity system, without adverse effect.
Detailed description of the invention
The present invention shares attached drawing 6 and opens.Wherein:
Fig. 1 is the small impedance transformer model schematic of electric system.
Fig. 2 is the flow chart that rectangular co-ordinate Newton Power Flow calculates.
Fig. 3 is the flow chart that 1 rectangular co-ordinate Newton Power Flow of patented method calculates.
Fig. 4 is the flow chart that 2 rectangular co-ordinate Newton Power Flow of patented method calculates.
Fig. 5 is the flow chart that rectangular co-ordinate Newton Power Flow of the present invention calculates.
Fig. 6 is the flow chart that the present invention forms node institute's chord road type array.
Specific embodiment
The present invention is described further with reference to the accompanying drawing.Small impedance transformer model according to figure 1, is adopted
The flow chart that the rectangular co-ordinate Newton Power Flow shown in Fig. 5-6 calculates, has carried out Load flow calculation to a practical large-scale power grid.
The practical large-scale power grid has 445 nodes, contains a large amount of small impedance branches.Wherein, the small impedance branches of x≤0.001 have 49
Item, the small impedance branches of x≤0.0001 have 41, and the small impedance branches of x≤0.00001 have 22.Wherein impedance value is the smallest
It is the small impedance branches l between node 118 and node 125118-125It is located at section for x=0.00000001, no-load voltage ratio k=0.9565, k
118 sides of point.The convergence precision of Load flow calculation is 0.00001.Calculate to verify the present invention containing resistance be not 0 small impedance branches
The convergence of electric system, small impedance branches l118-125、l60-122And l287-310Resistance be changed to r=0.0001.
As a comparison, while using following 3 kinds of control methods Load flow calculation has been carried out to the practical large-scale power grid:
Conventional method: conventional rectangular co-ordinate Newton Power Flow method；
Patented method 1: the patented method of Patent No. ZL201410315785.1；
Patented method 2: application No. is the patented methods of ZL201611094297.8.
The number of iterations the results are shown in Table 1.
The iteration result of the different trend methods of table 1
| Method | Conventional method | Patented method 1 | Patented method 2 | The method of the present invention |
| Iteration result | It does not restrain | 7 convergences | 6 convergences | 5 convergences |
Seen from table 1, for modified 445 node practical power systems example, conventional Cartesian coordinate Newton Power Flow
Method does not restrain, and the method for the present invention and existing patented method can restrain, but the number of iterations of the method for the present invention is more special than existing
Sharp method 1 is 2 times few, than existing patented method 2 few 1 times.
Different each secondary iteration maximum amount of unbalances of tidal current computing method are shown in Table 2.Unit is per unit value.
Each secondary iteration maximum amount of unbalance of the different trend methods of table 2
| Iteration serial number | Conventional method | Patented method 1 | Patented method 2 | The method of the present invention |
| 0 | -4754.570367135 | -4754.570367135 | -4754.570367135 | -4754.570367135 |
| 1 | -3451593.823720038 | -11.138394991 | -3.264368583 | 23.913925681 |
| 2 | -886651.468310079 | -6.163450054 | -0.715148045 | 3.050019341 |
| 3 | -222023.112200678 | -1.441071252 | -0.076847277 | 0.102604201 |
| 4 | -55754.415245002 | -0.106199006 | -0.002294590 | -0.000454516 |
| 5 | -13972.568194423 | -0.006353455 | -0.000017499 | -0.000000012 |
| 6 | -6386.835620506 | -0.000141863 | -0.000000001 | |
| 7 | -6585.38761914 | -0.000000062 | ||
| 8 | -378994.776907351 | |||
| 9 | -98508.025841226 | |||
| 10 | -37917.863557986 |
As shown in Table 2, maximum amount of unbalance is identical and very big before iteration for the first time for 4 kinds of methods.For the first time after iteration, existing patent
Method and this patent method maximum amount of unbalance significantly reduce, existing 1 iteration of patented method 7 times convergences；Existing patented method 2 changes
6 convergences of generation；This patent method maximum amount of unbalance reduces speed faster, iteration 5 times convergences；And the maximum of conventional method is uneven
Measurement then becomes larger, final to dissipate.
When each node power reactive power input value and Load flow calculation that the endpoint of small impedance branches is PV node restrain
Calculated value and initial calculation value are shown in Table 3.Unit is per unit value.
Calculated value and initial calculation value when the power supply reactive power input value and convergence of table 3PV node
| Node | Input value | Restrain calculated value | Initial calculation value |
| 22 | 1.80000 | 1.36829 | 0.15000 |
| 400 | 0.10000 | 0.69586 | 204.87496 |
| 439 | 0.80000 | 0.48861 | 525.04000 |
| 440 | 0.80000 | 0.48861 | 525.04000 |
It seen from table 3, is each node of PV node, power supply reactive power input value and trend for small impedance branches endpoint
Calculated value when calculating convergence has biggish difference, but the difference of calculated value when initial calculation value and Load flow calculation convergence is more
Greatly.Therefore for the first time iteration when, the endpoints of small impedance branches will be closed more with the real and imaginary parts that input value calculates Injection Current phasor
Reason.
The present invention can realize using any programming language and programmed environment, as C language, C++, FORTRAN,
Delphi etc..Developing environment can be using Visual C++, Borland C++Builder, Visual FORTRAN etc..
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. iteration small impedance branches endpoint changes the tidal current computing method of Jacobian matrix for the first time, it is characterised in that: including following
Step:
A, initial data and initialization voltage are inputted
Electric system node is divided into 3 classes: node active power and idle function by the characteristics of according to electric system node, Load flow calculation
The node that rate is known, node voltage amplitude and voltage phase angle are unknown is known as PQ node；Known to node active power and voltage magnitude,
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 node has
Function power and the unknown node of reactive power are known as balance nodes；
For voltage initialization using flat starting, i.e. the voltage real part of PV node and balance nodes draws definite value, and the voltage of PQ node is real
Portion takes 1.0；The imaginary part of all voltages all takes 0.0；Here unit uses per unit value；
B, two end node institute's chord road type array T are determined according to the size of branch resistance and reactance
Forming node institute's chord road type array, specific step is as follows:
B1, branch data is read in, small resistance threshold r is setminWith low reactance threshold value xmin；
B2, node institute's chord road type array T are reset；
B3, q=1 is enabled；
B4, first and last node number i and j, the resistance r, reactance x for taking branch q；
B5, judge whether to meet r≤rminAnd x≤xminCondition, if conditions are not met, going to step B7；
B6, T is enabledi=1, Tj=1；
B7, q=q+1 is enabled；
B8, judge whether q is greater than circuitry number l, if q goes to step B4 no more than l；Otherwise C is gone to step；
C, node admittance matrix is formed
If node i and the original self-conductance of node j with from susceptance be respectively Gi0、Bi0、Gj0、Bj0, increase between them one small
Self-admittance and transadmittance after impedance branch are respectively as follows:
In formula, Yii、YjjThe respectively self-admittance of node i and node j；YijFor the transadmittance between node i and node j；rij、xij
The resistance of small impedance branches and reactance respectively between node i and node j；K small impedance branches between node i and node j
No-load voltage ratio, if it is power transmission line branch, no-load voltage ratio k is 1；
D, iteration count t=0 is set；
E, power and voltage deviation are calculated, maximum amount of unbalance Δ W is soughtmax；
The power deviation calculation formula of PQ node are as follows:
In formula, Pis、QisRespectively node i given injection active power and reactive power；eiAnd fiThe respectively voltage of node i
The real and imaginary parts of phasor；ai、biRespectively node i calculating Injection Current phasor real and imaginary parts, be
In formula, n is the number of nodes of electric system；
When Load flow calculation is restrained, Δ P in formula (4)i、ΔQiAll level off to 0, therefore aiAnd biEqual to by given value PisAnd QisIt calculates
A outisAnd bis
The active power and voltage deviation calculation formula of PV node are as follows:
In formula, VisThe voltage magnitude given for node i；
Balance nodes are not involved in iterative calculation, do not need to calculate power deviation or voltage deviation；
Ask the value of maximum absolute value in each node power or voltage deviation, referred to as maximum amount of unbalance Δ Wmax；
F, judge maximum amount of unbalance absolute value | Δ Wmax| whether it is less than convergence precision ε；If it is less than convergence precision ε, step is executed
Rapid J；Otherwise, step G is executed；
G, Jacobian matrix J is formed
In addition to iteration for the first time, Jacobian matrix calculation method still uses conventional method；The Jacobian matrix calculating side of iteration for the first time
Method uses distinct methods according to the type that node connects branch；For the endpoint of small impedance branches, because using conventional method meter
Calculating Jacobian matrix will lead to Load flow calculation diverging, so calculating Injection Current using formula (6) when calculating Jacobian matrix element
The real and imaginary parts effect of phasor is preferable；For the endpoint of normal impedance branch, Jacobian matrix is still traditionally calculated
Element, i.e., the real part a of the node i Injection Current phasor in Jacobian matrix calculation formulaiWith imaginary part biIt is calculated by formula (5)；
Forming Jacobian matrix element, specific step is as follows:
Jacobian matrix element when G1, calculating i ≠ j；
As i ≠ j, the element calculation formula of Jacobian matrix J is as follows:
G2, i=1 is enabled；
G3, judge whether to meet t=0 and T simultaneouslyi=1 condition, if being unsatisfactory for going to step G4；If it is satisfied, then pressing formula (6)
The real part a of the Injection Current phasor of calculate node iiWith imaginary part bi, then go to step G5；
G4, by formula (5) calculate node i Injection Current phasor real part aiWith imaginary part bi；
Jacobian matrix element when G5, calculating i=j；
As i=j, the element calculation formula of Jacobian matrix J is as follows:
PQ saves knock type (14)-(17) and calculates Jacobian matrix element；PV node is calculated refined by formula (14), (15), (18), (19)
Than matrix element；Balance nodes do not calculate Jacobian matrix element；
G6, i=i+1 is enabled；
G7, judge whether i is greater than number of nodes n, if i goes to step G3 no more than n；Otherwise H is gone to step；
H, update equation and amendment voltage real part e, imaginary part f are solved
The fundamental equation (4) of Load flow calculation and (7) are Nonlinear System of Equations, are iteratively solved using successive Linearization Method；Linearly
Change obtained equation and be known as update equation, for seeking the correction amount of voltage real and imaginary parts；
Update equation are as follows:
In formula, J is Jacobian matrix；Δ P and Δ Q is respectively active power and reactive power deviation column vector；ΔV2For voltage amplitude
It is worth deviation column vector；Δ e and Δ f is respectively the real and imaginary parts correction amount column vector of voltage phasor；For wattful power
For rate departure function column vector to the local derviation matrix of voltage phasor real part column vector transposition, subscript T is transposition symbol；
Voltage correction formula are as follows:
In formula, subscript t indicates the t times iteration；
I, t=t+1, return step E is enabled to carry out next iteration；
J, output node and branch data.
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| CN104037764A (en) * | 2014-07-03 | 2014-09-10 | 大连海事大学 | Rectangular coordinate Newton method load flow calculation method with changeable Jacobian matrix |
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