WO2014114107A1

WO2014114107A1 - Method for optimizing optimal power flow of distributed generations

Info

Publication number: WO2014114107A1
Application number: PCT/CN2013/084269
Authority: WO
Inventors: 盛万兴; 刘科研; 程绳; 刘永梅
Original assignee: 国家电网公司; 中国电力科学研究院
Priority date: 2013-01-22
Filing date: 2013-09-26
Publication date: 2014-07-31
Also published as: CN103150606B; CN103150606A

Abstract

The present invention relates to a method for optimizing the optimal power flow of distributed generations, comprising the following steps: A, initializing variables in a distribution network; B, performing a power flow calculation on the distribution network; C, judging whether there is a circuit overload, and whether active and reactive power outputs of generators and the distributed generations cross the boundary; D, jumping to a step E if constraint equations are all met, otherwise, jumping to a step F; E, judging whether the value of an objective function is the smallest, if so, jumping to a step J, otherwise, jumping to a step F; F, correcting a loss correlation coefficient; G, calculating a Jacobean matrix and a Hessian matrix; H, creating a sub-problem of sequential quadratic programming, and solving search direction and step size; I, correcting the power output at a slack bus and the power output of each distributed generation, and jumping to the step B; and J, outputting an optimal power flow result. The method of the present invention provides a basis of calculation on access capacity for determining the access of the distributed generations to a distribution network, is simple in calculation and low in complexity, and can rapidly calculate the power outputs of the distributed generations.

Description

A distributed power source optimal power flow optimization method

Technical field

The invention relates to a power system calculation optimization method under distributed power access, and particularly relates to a distributed power source optimal power flow optimization method. Background technique

In recent years, distributed power (DG) has received strong support from national policies for its many advantages, and has become an important development direction in the energy field. It also provides new options for power grid planning. However, the rapid development of distributed generation and the large number of grid-connected operations have made distribution network planning more uncertain than ever. In order to generate an optimized distributed power planning strategy, it is necessary to analyze and calculate the accessible capacity and requirements of the distributed power source.

The State Grid Corporation has specified the technical requirements for the construction of new or expanded distributed power supplies connected to the grid with voltage levels of 35kV and below. The short-circuit current and permeability of the distributed power supply are clearly defined, but it is still difficult to determine the specific Distributed power output capacity, especially in complex network configurations with different network topologies and different load sizes.

Optimal Power Flow (OPF) is an effective analytical tool for solving operational and planning problems in power systems. The typical optimal power flow is based on the power balance equation, generator load limit, and line load limits to minimize power generation costs or maximize social benefits. In the past, OPF analysis and calculations were mostly used to minimize the power generation cost of the transmission grid. In recent years, the research and application of OPF has expanded to the analysis of complex distribution networks. In this type of research method, the optimization objectives are usually: 1) DG has the lowest power generation cost; 2) maximizes the active output of DG; 3) minimizes the active line loss; 4) multi-objective optimization of the combination of the above optimization objectives.

The calculation methods of OPF problems include linear programming methods, quadratic programming methods, nonlinear programming methods and intelligent algorithms. When the objective function is quadratic and its constraint is linear, it can be solved by the quadratic programming method. For the OPF problem with DG, the optimal solution can be obtained by solving a series of quadratic programming problems. Summary of the invention

The present invention provides a method for optimizing the optimal power flow of a distributed power supply in the case where the distributed power output capacity is difficult to be clearly determined. Based on the optimal power flow of the sequence quadratic programming, the distributed power access capacity in the distribution network is solved. The optimization power flow is applied to the planning and optimization of distributed power supply, with the minimum power generation cost as the optimization goal, taking into account the network line constraints and voltage safety, using the sequence quadratic programming to solve the optimization calculation problem, and the distributed power supply is given. The calculation method for access capacity of the distribution network.

Replacement page (Article 26) The object of the present invention is achieved by the following technical solutions - The present invention provides a distributed power source optimal power flow optimization method, which is improved in that the method includes the following

A. Initialize variables in the power distribution network;

B. Perform power flow calculation on the distribution network;

C. Determine whether the line is overloaded, whether the generator and the distributed power source have a reactive power output that is out of bounds;

D. If the constraint equations of the distribution network system are all satisfied, skip to step E, otherwise skip to step F;

E, determine whether the value of the objective function is the smallest, if it is the minimum, jump to step J, otherwise skip to step F;

F. Repair the network loss correlation coefficient;

G, calculating the Jacobian matrix and the Hessian matrix;

H, forming a sequence quadratic programming sub-problem, and solving the search direction and step size of the sequence quadratic programming sub-question;

I, modify the balance node bus output and the distributed power output, jump to step B;

J. Output the optimal power flow result.

In the step A, the variables in the power distribution network include the network topology and number, the bus voltage, the node load, the secondary planning parameters μ and s, and the initial solution of the distributed power output ^ where is the preset floating point Type _ number, μ is the Lagrange latch coefficient.

Wherein, in the step C, determining whether the line is overloaded and whether the generator and the distributed power source reactive power output exceed the upper and lower limits are as follows:

P!T < P _nr , ≤P"

( 1 );

Among them, for the active output of the first distributed power supply, ^^ and ⁷ ^^ are the upper and lower limits of the active output of the first distributed power supply, ^β : the reactive power of the first distributed power supply, ^ρ and respectively The upper and lower limits of the reactive power of the first distributed power supply; the power flow on the line, the line power power constraint, 'and the node voltages on nodes ζ and J respectively; ^G 'j and ^β ' are nodes i and 】 Conductance and susceptance on.

Wherein, in the step D, the constraint equation of the distribution network system is represented by the following expression group:

'-' (4) ;

Replacement page (Article 26)

Where: ^P " is the total active load of the system, which is the total active network loss of the system; ^β "is the total reactive load of the system, ^Ql is the total reactive power loss of the system; ^P , and ² are the active power at the substation respectively Output and reactive compensation.

Wherein, in the step E, the secondary cost model is selected as the cost model of the distributed power source, and the objective function of the cost model is expressed by the following formula:

(6); where: ^C ', ^b ', ^α ' are the cost coefficients of the distributed power supply ^, respectively, and ^e and ^b are the cost coefficients at the relaxed bus;

Calculate the minimum value of the objective function using (6); assume that the initial output forces at the distributed power supply and the slack bus are respectively , and the initial output adjustment increments are:

(7);

f _IK

+ a _K Al + (2a, j + b _s )AP

(8);

Change the objective function to an incremental form, represented by the following expression: i=\

= ΪΜ,Ά, ) -f C )} + 14 (P ) -k (^)}

(9);

Where: [ί·] = [Α,ϋ ₂ ,···, , c _v ], c, =2a,P? +b , H is the Hessian matrix H )x

The active balance equation of the distribution network system is as follows:

(10);

Replacement page (Article 26) Where: ^ is the total load of the distribution network system, which is the total network loss of the distribution network system; for the formula (10), the flat guidance is: dP /,) (;,

(11);

Into a simplification:

Where: ^ is the active gain at the relaxation bus, ^: ⁰ — ⁵ ^ ⁵ ^') is the correlation coefficient of the network loss. Wherein, in the step F, the network loss correlation coefficient ^ ^{= (1} - ^{δ /} · ^{/ δ /} ^ ') is repaired.

Wherein, in the step G, the Hessian matrix is calculated by using the expression (9); and the Jacobian matrix is calculated by using the expression ^^( )i/ + _C (xJ = 0;

When the distributed power output changes, the power flowing through the line changes, each line has its apparent power limit value, and the line apparent power constraint inequality becomes incremental:

△S <AS ^x =S - S (13); where: ^Δ is the increment of the apparent power square of the line, and consists of active and reactive power increments;

Define the line power sensitivity matrix of the distribution network system /):

AP _h ^DxAP _lx; (14);

AQ _h =DxAQ _a; (15); where: ^ and 3⁄4 are the active power and reactive power flowing through the line, and Δρ _{Λ is} its incremental value; the sensitivity matrix is characterized by the distributed power supply node active or When reactive power changes, the line flows through the amount of active and reactive power changes; let F be the path matrix of each distributed power node, then have the following equation:

A(P _h /U _h ) = Tx(AP _lx; /U _lx: ) (16);

HQ _h ) = T (AQ _DG /U _DG ) (17);

Where: is the voltage amplitude of the first segment of branch b, ^ ⁷ "'' is the distributed power supply voltage amplitude; when, there are the following expressions:

RxAP^+X AQ^^ (18);

7? and the real and imaginary parts of the row corresponding to the distributed power supply node in the node impedance matrix of the distribution network system; define the matrix M=Γ'χ, then the equation (17) is written as:

AQ _{D (} ^MxAP _lx; (19); Replacement page (Rule 26) When the reactive power of the PV type node reaches the limit, the corresponding row of the PV type node in the matrix M is set to zero; for the increment of the apparent power square of the line:

AS = 2x P _b X AP _b +2xQ _b x AQ _b + AP _b ² <AS^ (20)

Wherein, in the step H, according to the expressions (13) ~ (20) in the step G, the optimal power flow model of the distributed power active as the control quantity is as follows:

1

Min = c · + - Δ^' . Η . AP _tl

S.t. J β, · + 0

(2xP _b xZ) + 2xQ _b xx )x ΑΡ _Κ . < AS ²

A ^min < AP < ΛΡ

;x - ^ar na - ^ar ix: (21 );

The above formula (21) is the problem of sequence quadratic programming;

The sequence quadratic subproblem is represented by the following expression set: min ( Vg(x _A ) ⁷ ) st

+ c(x _k ) = 0 (22);

x _t -x _k ≤d≤x _u -x _k

Where: for the search direction, ^^ is the derivative, ^ is the Jacobian matrix of c, for transposition; ^β * is the Hessian matrix approximation of the Lagrangian latch function; is 歩 long; indicates the first search direction of the loop iteration , it is a vector; d ^T is the transposition of the search direction, ^Χ 'and ^X ' are the upper and lower limits respectively, and are transposed;

The convergence conditions for expression sets (21) and (22) are:

(23); where: f is a preset floating point positive number.

Wherein, in the step I, the balance node bus output and the distributed power output are corrected by using the sub-form ₊₁ = x _t + 4 in the expression group (22).

Wherein, in the step J, the optimal power flow output result is the obtained output value of the balance node bus and the distributed power output value, and the balance node bus line corresponds to the emergence end of the substation in the distribution network. Compared with the prior art, the beneficial effects achieved by the present invention are: Replacement page (Article 26) 1) The distributed power source optimal power flow optimization method provided by the present invention solves the distributed power supply access capacity in the distribution network based on the optimal power flow of the sequence quadratic programming. The optimization power flow is applied to the planning and optimization of distributed power supply, with the minimum power generation cost as the optimization goal, taking into account the network line constraints and voltage safety, using the sequence quadratic programming to solve the optimization calculation problem, and the distributed power supply is given. The calculation method for access capacity of the distribution network.

2) The invention provides a basis for calculating the access capacity for determining a distributed power supply distribution network;

3) The method proposed by the invention has simple calculation and low computational complexity, and can quickly calculate the output of the distributed power source;

4) The distributed power source in the present invention can cover photovoltaic, micro gas turbine, micro diesel generator, wind energy, etc., and the distributed power source can be flexibly selected. DRAWINGS

1 is a flow chart of a distributed power supply optimal power flow optimization method provided by the present invention. detailed description

The specific embodiments of the present invention are further described in detail below with reference to the accompanying drawings.

Here, the problem is the optimal power flow problem with the goal of minimum generator cost. It consists of two parts, one is the cost of a conventional generator, and the other is the cost of a distributed power supply. If the balance node in the distribution network is not a conventional generator, then the price of power generation at the balance node bus is considered to be a virtual price relative to the distributed power source in the network. This is in line with the principle that distribution networks are always expected to have as much output power as possible under network conditions.

The flow of the distributed power optimal flow optimization method provided by the present invention is as shown in FIG. 1 , and includes the following steps:

A. Initialize variables in the power distribution network;

Such as network topology and number, bus voltage, node load and other information as well as quadratic programming parameters μ, s and the initial solution of distributed power output x ^(Q '_; where f is the preset floating point positive number, μ is pulling Grande coefficient.

Β, power flow calculation for distribution network; power flow calculation includes calculation of voltage, current, power and other parameters.

C. Determine whether the line is overloaded, whether the generator and distributed power supply have a reactive power output that is out of bounds:

The upper and lower limits for judging whether the line is overloaded and whether the generator and distributed power source reactive power output crosses the boundary are as follows:

- ( 1 ); ( 2 );

\ = ^ ^G „- ^v ^ (G" ^{cos θ} „ + ⁱⁿ )1 ^{≤ s} r ( ₃ ) ; where ""' is the active output of the first distributed power supply, ^ρ and the first distributed power supply respectively Replacement page (Article 26) The upper and lower limits of the active output are the reactive power of the first distributed power source, and the upper and lower limits of the reactive power of the first distributed power supply respectively; for the power flow on the line, '' ^λ _3⁄4 line power power constraint, and Node/and

The node voltage on J; ^G "and ^β " are the conductance and susceptance at node i and respectively.

D. If the constraint equations of the distribution network system are all satisfied, skip to step E, otherwise skip to step F:

The constraint equations for distribution system systems are represented by the following set of expressions:

_{∑P IXJI} + P _s =P _n +P _L

'='(4);

'='(5); where: is the total active load of the system, which is the total active network loss of the system; ^ρ "is the total reactive load of the system, ^Qi is the total reactive power loss of the system; ^p , and ^ρ , respectively It is the active output and reactive power compensation at the substation.

Ε, determine whether the value of the objective function is the smallest. If it is the minimum, jump to step J, otherwise skip to step F:

The price coefficient of distributed power supply is usually different. In this paper, the quadratic cost model is used as the cost model of distributed power supply. The objective function of the problem is as follows - min F(x, u) = f _lx .(x, u) + f,, (x, u)

'(6); where: ^C ', ^b ', ' are the cost coefficients of the distributed power supply, respectively, and ^{b fl} , respectively, the cost coefficient at the relaxed bus;

Calculate the minimum value of the objective function using (6); To convert equation (6) into an incremental model, assume that the initial output of each power supply is sum, and the output adjustment increment is sum and ^, then - ί, Α + Δ^ ,) = 4 _; ( Χ +« _; ( ₇ ) _;

f _l>r (l +AP = f _s (^) + a _s M +(2a _s ff +b _s )AP _{v (8)} ; The objective function is changed to an incremental form, represented by the following expression:

Replacement page (Article 26)

(9);

Where: [C] = [ _CI , C ₂ ,...,C _NDG ,C _s ], c =2a,P^b , H is the Hessen matrix H^/^^+^^+^ '2α,, i = j

h, =

[Δ ] ^Γ =[Κ ₂ ,··.,Δ^),ΔΡ _ν ] The active balance equation of the distribution network system is as follows:

(10); Where: ^Ρβ is the total load of the distribution network system, Α is the total network loss of the distribution network system; and ( ^p ) is obtained by the formula (10):

' (11);

Further simplification is:

Where: ^ is the active gain at the relaxed bus, and A^G— is the correlation coefficient of the network loss.

F, repair IH network loss correlation coefficient A = 1_3^ /dP _{D (} .)-,

G. Calculate the Jacobian matrix and the Hessian matrix:

Use the expression (9) to calculate the Hessian matrix; use the expression)^ + ) = 0 to calculate the Jacobian matrix; when the distributed power supply has a change in the output force, the power flowing through the line will change, and each line has its own view. The power limit turns the line apparent power constraint inequality into an incremental form -

AS^ <AS ^nax2 =S^ -S (13); where: ^Δ is the increment of the square power of the line apparent power, consisting of active and reactive power increments;

Define the line power sensitivity matrix of the distribution network system

AP^DxAP^ (14);

AQ^DxAQ^ (15); where: active power and reactive power flowing through the line, ^ and 3⁄4 are their incremental values; sensitivity matrix replacement page (rule 26) It is characterized by the amount of change in active and reactive power flowing through the line when the distributed power supply node has active or reactive power changes. In a radial distribution network, these two matrices are closely related to the path matrix. If the path matrix is distributed for each distributed power node, the following equation holds:

A(P _h /U _h ) = Tx(AP _lx; /U _lx; ) (16)

A(Q _h /U _h ) = Tx(AQ _DG /U _lx; ) (17)

^ is the branch voltage b first segment voltage amplitude, which is the distributed power supply voltage amplitude, considering that the voltage of each node of the network is near the rated voltage of the line, and the integrated equations (14) and (15) have 0 Γ. In addition, since the reactive power of the PV type DG is not independently controlled, when the PV type DG changes in power, the reactive power will be adjusted within the constraint range so that the node voltage amplitude remains unchanged, ignoring the imaginary part of the node voltage. Influence, the following equation is established:

RxAP _lx .+XxAQ _D( . =0 (18); R and X are the real and imaginary parts of the row of the distributed power nodes in the system node impedance matrix.

AQ _/x; ^MxAP _IXJ (19);

When the reactive power of a PV-type node has reached the limit, the corresponding row of the PV-type node in the M-matrix should be set to zero. For the increment of the apparent power square of the line:

(20) H, form a sequence quadratic programming sub-problem, and solve the sequence quadratic programming sub-question search direction and step size:

Slightly the squared term, according to the expressions (13) ~ (20) in step G, the optimal power flow model that forms the distributed power active as the control quantity is as follows: minF = c - AP _K + Δ . Η . Δ _Κ

(2xP _b xZ) + 2xQ _b xx )x AP _D( . < AS^

As shown above, the optimal power flow OPF problem becomes a problem of sequential quadratic programming, and the vector =[^ ^c is the vector to be solved.

The sequence quadratic subproblem is represented by the following set of expressions:

Replacement page (Article 26) (twenty two );

Where: ^ is the search direction, ^ is, derivative, ^ is the Jacobian matrix of c, is the transposition of ^; ^β * is the Hessian matrix approximation of the Lagrangian function; is the length of the ;; Search direction, which is a vector; d ^T is the transposition of the search direction, ^Χ 'and ^X ' are the upper and lower limits respectively, and are transposed;

The convergence conditions for expression groups (21) and (22) are:

I | ≤ ( 23 );

Where: f is the default floating point number.

I. Correct the balance node bus output and each distributed power output, and jump to step B: In step I, use the subroutine x _+l = 3⁄4 + ^ in the expression group (22) to correct the balance node bus. Output and output of each distributed power supply.

J. Output optimal power flow result: The optimal power flow output result is the output value of the balanced node busbar and the output power output value. In the distribution network, the equilibrium node busbar corresponds to the emergence end of the substation.

The invention provides a basis for calculating the access capacity for determining the distributed power supply distribution network; the method of the invention has simple calculation and low complexity, and can quickly calculate the output of the distributed power source.

It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limited thereto. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the present invention can still be The invention is to be construed as being limited to the scope of the appended claims.

Replacement page (Article 26)

Claims

Rights request

A distributed power source optimal power flow optimization method, characterized in that the method comprises the following steps:

A. Initialize variables in the power distribution network;

B. Perform power flow calculation on the distribution network:

D. If the constraint equations of the distribution network system are all satisfied, skip to step E, otherwise skip to step F _;

F. Correct the network loss correlation coefficient;

G, calculating the Jacobian matrix and the Hessian matrix;

H, forming a sequence quadratic programming sub-problem, and solving the search direction and length of the sequence quadratic programming sub-question;

I. Correct the output of the balance node bus and the output of each distributed power supply, and jump to step B;

J. Output the optimal power flow result.

2. The distributed power optimal power flow optimization method according to claim 1, wherein in the step A, variables in the power distribution network include network topology and number, bus voltage, node load, and secondary planning. The initial solutions for the parameters μ and f and the distributed power output ^ where s is the preset floating point positive number and μ is the Lagrangian coefficient.

3. The distributed power source optimal power flow optimization method according to claim 1, wherein in the step C, determining whether the line is overloaded and whether the generator and the distributed power source reactive power output exceed the upper and lower limits are as follows: :

Pi ship < p max

- ( 1 );

Quel ^≤ QDG, - Qna, ( 2 );

S _tl | = |Π ^ν ' ^ν Λ , cos θ _υ + Β _υ sin θ" )| <

>max

Where x'' is the active output of the first distributed power supply, ''and 1⁄2 '' are the upper and lower limits of the active output of the first distributed power supply, respectively, the reactive output of the first distributed power supply, ^β and respectively The upper and lower limits of the reactive power of the first distributed power source; the power flow on the line, the line power power constraint, and the node voltages on the nodes and respectively; ^G "and ^B " are the conductance of the nodes and j, respectively. Density.

4. The distributed power optimal power flow optimization method according to claim 1, wherein in the step D, the constraint equation of the distribution network system is represented by the following expression group:

Replacement page (Article 26) (4);

∑Q _(:i +Q _s -Q + Q _l

(5); where: ⁷ ^ is the total active load of the system, ^{Ρ /} is the total active network loss of the system; ² " is the total reactive load of the system, ^Q L is the total reactive power loss of the system; and ^, respectively It is the active output and reactive power compensation at the substation.

The distributed power optimal power flow optimization method according to claim 1, wherein in the step E, the secondary cost model is selected as the cost model of the distributed power source, and the objective function of the cost model is as follows: Indicates:

Min F(x, )

u) + _;; ; ( , u)

∑(c, +bP _IX!: +a,P^) ₊ (c _{s +} bP ₊ aP )

(6);

Where: c', b', "'the cost coefficient of the distributed power supply, respectively, and ^b s , ", respectively, the cost coefficient at the relaxed bus;

Calculate the minimum value of the objective function using (6); assume that the initial output forces at the distributed power supply and the slack bus are respectively and the initial output adjustment increments are

^"' and ^,, then:

Πϋ (7);

+ a _s Al +(2a _x l +b _s )AP _x

(8);

The objective function is changed to an incremental shape, represented by the following expression:

c][AP]+-[AP]' H[AP]

(9);

among them:

, c,], c, =2fl,f. +6, _; // is the Hessian matrix H = { },

The active balance equation of the distribution network system is as follows:

Replacement page (Article 26)

(10); Where: for the total load of the distribution network system, for the total network loss of the distribution network system; for the type no) to obtain ^P « flat guide: ι=ι ι=ι °"DG,

(11);

Further simplification is:

P PDG +

=— _{( 12} ). Where: ^Δ ^ is the active increment at the relaxation bus, and ^^(^ ⁵ ^ ⁵ ^^) is the correlation coefficient of the network loss.

6. The distributed power optimal power flow optimization method according to claim 1, wherein in the step F, the network loss correlation coefficient Α ^{= (1_δ) is corrected} .

7. The distributed power optimal power flow optimization method according to claim 1, wherein in the step G, the Hessian matrix is calculated by using the expression (9); and the expression '(x _A )i/ is used. + _C (xJ = 0 calculates the Jacobian matrix; when the distributed power supply's active output changes, the power flowing through the line will change, each line has its apparent power limit value, and the line apparent power constraint inequality becomes increased. The quantity forms are:

AS^ <AS ^nax2 =S _A ^max2 -S^ (13); where: ^Δ is the increment of the square power of the apparent power of the line, consisting of active and reactive power increments;

Define the line power sensitivity matrix of the distribution network system

AP^D AP^ (14);

AQ^D AQ^ (15); where: ^ and 3⁄4 are the active power and reactive power flowing through the line, Δ / ^ and Δ3⁄4 are their incremental values; the sensitivity matrix is characterized by the distributed power node active When the reactive power changes, the line flows through the active and reactive changes. For the path matrix of each distributed power node, there are the following equations:

(16);

Qb'm iAQ D (17);

Where: is the voltage amplitude of the first segment of branch b, ^∞ is the distributed power supply voltage amplitude; D«T, has the following expression:

=0 (18); and the real and imaginary parts of the row corresponding to the distributed power supply node in the node impedance matrix of the distribution network system; replacement page (Article 26) Define the matrix M= Γ ¹ _X Jr, then the equation (17) is written as:

AQ^ ^MxAP^ (19); When the PV type node reaches the limit, the corresponding row of the PV type node in the matrix M is set to zero; for the line apparent power squared increments are:

AS = 2xP _b x'AP _b +2xQ _b xAQ _b +AP _b ² +A </S^ (20)

The distributed power optimal power flow optimization method according to claim 1, wherein in the step H, the distributed power supply is formed according to the expression (13) (20) in the step G. The optimal power flow model of the control quantity is as follows:

1

Min = c · AP _I{ + - AP, _t ' . H · AP _K st ^β, -ΑΡ _οα +AP _s = 0

(2xP _b x£» + 2xQ _b x M)x P _D( , < A ^

ΛΡ < A < A ^max

(twenty one );

The above formula (21) is the sequence quadratic programming problem;

The sequence quadratic programming subproblem is represented by the following expression set: m(^d' B _k d + Vg(x _k )' d) st A' (x _k )d + c(x _k ) = 0 (22) ;

x, -x _k <d≤x _u -x _k

Xk+\ = + d _k where: is the search direction, ^¥ is ^/ derivative, ^ is the Jacobian matrix of ^, is the transposition of ^; ^β * is Lagrangian

The Hessian matrix approximation of the R function; /1 is the length of the ;; represents the search direction of the loop iteration, it is a vector; ^d ' ^r is the transposition of the search direction ^, ^Χ ' and ^X " are the upper and lower limits of ^ respectively , transposed;

The convergence conditions for expression groups (21) and (22) are:

|dj|≤ (23); where: s is the preset floating-point positive number.

9. The distributed power optimal power flow optimization method according to claim 1, wherein in the step I, the replacement page (Article 26) Use the subform in expression group (22); ^ , = +4A to correct the output of the balanced node bus and the distributed power output.

The distributed power source optimal power flow optimization method according to claim 1, wherein in the step J, the optimal power flow output result is the obtained output value of the balanced node bus and the distributed power output. The value, in the distribution network, the node of the balance node corresponds to the emergence end of the substation.

Replacement page (Article 26)