CN106329537A - Reactive power optimization method suitable for large-grid automatic voltage control - Google Patents

Reactive power optimization method suitable for large-grid automatic voltage control Download PDF

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CN106329537A
CN106329537A CN201510341645.6A CN201510341645A CN106329537A CN 106329537 A CN106329537 A CN 106329537A CN 201510341645 A CN201510341645 A CN 201510341645A CN 106329537 A CN106329537 A CN 106329537A
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represent
voltage
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sigma
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CN106329537B (en
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韩巍
丁汀
蒲天骄
王伟
李时光
王子安
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State Grid Corp of China SGCC
State Grid Zhejiang Electric Power Co Ltd
China Electric Power Research Institute Co Ltd CEPRI
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
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    • Y02E40/30Reactive power compensation

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Abstract

The invention provides a reactive power optimization method suitable for large-grid automatic voltage control, and the method comprises the following steps: determining a voltage stabilizing index of a branch circuit; building a reactive power optimization model; employing an internal point method to solve the reactive power optimization model. Aiming at a problem of voltage stabilizing in a power grid and a problem that the problem of voltage stabilizing is usually local, the method analyzes the voltage stabilizing index of the branch circuit, and improves the voltage stability margin of a region through the targeted reduction of the voltage stabilizing index of the branch circuit in the region in a target function of the optimization model.

Description

A kind of idle work optimization method adapting to bulk power grid automatism voltage control
Technical field
The invention belongs to technical field of electric power automation, be specifically related to a kind of idle work optimization side adapting to bulk power grid automatism voltage control Method.
Background technology
The core of the automatism voltage control of bulk power grid is that the idle work optimization of power system calculates.Idle work optimization is in optimal load flow Item typical problem.Traditional bulk power grid automatism voltage control is under given trend section, i.e. the network topology of system and parameter, Meritorious and idle, the generated power of load are exerted oneself when thinking fixing, run putting equipment in service condition and system mode meeting system In the case of parameter range of operation, generator terminal voltage, reactive-load compensation equipment are thrown and are moved back and the gear regulation of adjustable transformer, Change the reactive power distribution of system with this, thus reduce the network loss of system.
The at present Reactive Power Optimazation Problem of extensive practical power systems, widely used is nonlinear interior-point method carries out direct solution and By two kinds of technology paths of district and grade control.The method of degree and zoning stresses the effectiveness to power grid control, on electrical network analysis More weak.Due to subregion, between setting area, between controlled quentity controlled variable and quantity of state and region outer control amount and quantity of state, nothing is straight by force Connect impact or weak impact, but interregional in reality be interconnection or the controlled quentity controlled variable adhering to two regions separately of interconnection region and quantity of state Also it is strong correlation, therefore, does not sometimes ensure that its control direction is directed towards optimal direction regulation.Nonlinear interior-point method stresses Electrical network is directly optimized analysis, and owing to directly retraining with power flow equation, therefore producing control strategy is also also to be to meet trend Equation.The data provided yet with the appearance of discrete device and state estimation occur there will be when deviation is bigger solve difficulty and Being difficult to the problem solved, therefore, prior art also needs to improve.
Summary of the invention
In order to overcome above-mentioned the deficiencies in the prior art, the present invention provides a kind of idle work optimization side adapting to bulk power grid automatism voltage control Method, specifically adopts the following technical scheme that:
The present invention provides a kind of idle work optimization method adapting to bulk power grid automatism voltage control, said method comprising the steps of:
Step 1: determine the voltage stability index of branch road;
Step 2: set up idle work optimization model;
Step 3: use interior point method to solve idle work optimization model.
Described step 1 specifically includes following steps:
Step 1-1: calculate the voltage stability margin L of branch road ij between node i and node jij, the voltage as branch road ij is steady Determine index;
Step 1-2: judge LijWhether exceeding threshold value T, if exceeding, respective branch being contributed to set of fingers M.
In described step 1-1, between node i and node j, the voltage stability margin of branch road ij is LijIt is expressed as:
L i j = 4 [ 1 - 0.5 B ( X - R ) ] [ P j ( X + R ) + Q j ( X - R ) ] U i 2 ( 1 + sinδ i j ) - - - ( 1 )
Wherein, R and X represents resistance and the reactance of branch road ij, δijRepresent the phase difference of voltage of node i and node j, UiRepresent The voltage magnitude of node i, PjAnd QjRepresent outflow active power and the reactive power of node j respectively;
In described step 2, idle work optimization model includes idle work optimization object function and idle work optimization constraints.
Described idle work optimization constraints includes equality constraint and inequality constraints;
Described equality constraint includes trend equality constraint, transformer voltage ratio equality constraint and capacitive reactance device equality constraint;
Described inequality constraints includes that node voltage inequality constraints, voltage slack inequality constraints and generator reactive are exerted oneself not Equality constraint.
Described idle work optimization object function is expressed as:
min f ( x ) = Σ ( i , j ) ∈ M G i j ( U i 2 + U j 2 - 2 U i U j cosδ i j ) + ω Σ i = 1 N S i 2 + ψ Σ m ∈ M L i j m - - - ( 2 )
Wherein, f (x) represents idle work optimization object function, and M represents set of fingers, UiAnd UjRepresent node i and node j respectively Voltage magnitude, GijRepresent the conductance of branch road ij, δijRepresenting the phase difference of voltage of node i and node j, N represents node set, M represents that voltage stability margin exceedes the branch road of threshold value;SiRepresent the voltage slack of node i,Represent the voltage of branch road ij Stability margin, ω represents variation weight, and ψ represents voltage stability index weight.
In described equality constraint, have:
(1) trend equality constraint is expressed as:
P G , i - P D , i - U i ΣU j ( G i j cosδ i j + B i j sinδ i j ) = 0 i ∈ N Q G , i - Q D , i - U i ΣU j ( G i j sinδ i j + B i j cosδ i j ) = 0 i ∈ N - - - ( 3 )
Wherein, PG,iAnd QG,iRepresent that at node i, electromotor injects active power and reactive power, P respectivelyD,iAnd QD,iRepresent respectively Generated power load and load or burden without work, U at node iiAnd UjRepresent node i and the voltage magnitude of node j, G respectivelyijAnd BijPoint Not Biao Shi the conductance of branch road ij and susceptance, N represents node set, δijFor the phase difference of voltage of node i Yu node j, and δijij, Wherein θi、θjIt is respectively node i, the voltage phase angle of j;
(2) transformer voltage ratio equality constraint is expressed as:
(Tk-Tk,min)(Tk,max-Tk)=0 k ∈ ST (4)
Wherein, TkRepresent the no-load voltage ratio of kth transformator, Tk,maxAnd Tk,minRepresent the no-load voltage ratio bound of kth transformator, S respectivelyT Indication transformer set;
(3) capacitive reactance device equality constraint is expressed as:
(Bh-Bh,min)(Bh,max-Bh)=0 h ∈ SB (5)
Wherein, BhRepresent the susceptance of the h capacitive reactance device, Bh,maxAnd Bh,minRepresent the susceptance bound of the h capacitive reactance device respectively, SBRepresent capacitive reactance device set.
In described inequality constraints, have:
(1) node voltage inequality constraints is expressed as:
Ui,min+Si≤Ui≤Ui,max-Si i∈N (7)
Wherein, SiRepresent the voltage slack of node i, UiRepresent the voltage magnitude of node i, Ui,maxAnd Ui,minRepresent joint respectively The voltage magnitude bound of some i, N represents node set;
(2) inequality constraints of voltage slack is expressed as:
Si≥0 i∈N (8)
Wherein, SiRepresenting the voltage slack of node i, N represents node set;
(3) generator reactive inequality constraints of exerting oneself is expressed as:
QGi,min≤QG,i≤QGi,max i∈N (9)
Wherein, QG,iRepresent that at node i, electromotor injects reactive power, Q respectivelyGi,maxAnd QGi,minRepresent respectively and generate electricity at node i Machine injects reactive power bound, and N represents node set.
Described step 3 specifically includes following steps:
Step 3-1: first idle work optimization model is divided into discrete device equality constraint and continuous quantity Optimized model;
Step 3-2: continuous quantity Optimized model is expressed as:
min f ( x ) = Σ ( i , j ) ∈ M G i j ( U i 2 + U j 2 - 2 U i U j cosδ i j ) + ω Σ i = 1 N S i 2 + ψ Σ m ∈ M L i j m ΔP i = P G , i - P D , i - U i T k , i ΣU j ( G i j cosδ i j + B i j sinδ i j ) = 0 , i ∈ N ΔQ i = Q G , i + B h , i U i 2 - Q D , i - U i T k , i ΣU j ( G i j sinδ i j - B i j cosδ i j ) = 0 , i ∈ N U i , min + S i ≤ U i ≤ U i , max - S i , i ∈ N S i ≥ 0 , i ∈ N Q G i , min ≤ Q G , i ≤ Q G i , max , i ∈ N - - - ( 10 )
Wherein, f (x) represents idle work optimization object function, and M represents set of fingers, UiAnd UjRepresent node i and node j respectively Voltage magnitude, GijRepresent the conductance of branch road ij, δijRepresenting the phase difference of voltage of node i and node j, N represents node set, M represents that voltage stability margin exceedes the branch road of threshold value;SiRepresent the voltage slack of node i,Represent the voltage of branch road ij Stability margin, ω represents variation weight, and ψ represents voltage stability index weight, Bh,iRepresent the h capacitive reactance device at node i Susceptance, Tk,iRepresent the no-load voltage ratio of kth transformator, Δ P at node ii、ΔQiRepresent the deviation and idle of gaining merit at node i respectively Deviation;
Definition vector x=[QG,1,…,QG,i,…,QG,N,S1,…,Si,…,SN,U1,…,Ui,…,UN1,…,θi,…,θN]T, for continuous quantity Optimized model forms unconfined majorized function L, has:
L = f ( x ) - Σ i ∈ N y p i ΔP i - Σ i ∈ N y q i ΔQ i - Σ i ∈ N z i ( U i - U i , min - S i - l i ) - Σ i ∈ N w i ( U i - U i , max + S i + u i ) - Σ i ∈ S G z i ( Q G , i - U i , min - l i ) - Σ i ∈ S G w i ( U i - U i , max + u i ) - μ Σ i ∈ ( N + S G ) ln ( l i ) - μ Σ i ∈ ( N + S G ) ln ( u i ) - - - ( 11 )
Wherein, SGRepresenting electromotor node, μ represents disturbance variable, and μ >=0;li、uiRepresent respectively under the voltage of node i Slack variable in slack variable and voltage, ypi、yqi、zi、wiRepresent the lagrange's variable of node i, definition vector L=[l1,l2,……,lr], u=[u1,u2,……,ur], vector y={yp1,…ypi,…,ypN,yq1,…,yqi,…,yqN, vector Z=[z1,z2,……,zr], vector w=[w1,w2,……,wr], r represents inequality number;
Then meet:
L x = ▿ x f ( x ) - ▿ x h ( x ) y - ▿ x g ( x ) ( z + w ) = 0 L y = h ( x ) = 0 L z = g ( x ) - l - g ‾ = 0 L w = g ( x ) + u - g ‾ = 0 L l = L Z E + μ E = 0 L u = U W E - μ E = 0 - - - ( 12 )
Wherein, LxRepresent the majorized function L local derviation to vector x, LyRepresent the majorized function L local derviation to vector y, LzRepresent The majorized function L local derviation to vector z, LwRepresent the majorized function L local derviation to vector w, LlRepresent that majorized function L is to vector The local derviation of l, LuRepresent the majorized function L local derviation to vector u,xRepresent idle work optimization object function f (x) inclined to vector x Lead, trend equality constraint vector h (x)={ Δ P1,…,ΔPi,…,ΔPN, Δ Q1,…,ΔQi,…,ΔQN, g (x) represents inequality about Shu Xiangliang,Represent the inequality constraints upper limit,gRepresenting inequality constraints lower limit, L, Z, U, W are respectively li、zi、ui、wi The r of composition ties up diagonal matrix, and the r that E is ties up unit matrix;
Step 3-3: described discrete device equality constraint includes transformer voltage ratio equality constraint and capacitive reactance device equality constraint;
Increase duality gapThen have:
T k ( T k - T k , min ) ( T k , max - T k ) - C g a p = 0 k ∈ S T B h ( B h - B h , min ) ( B h , max - B h ) - C g a p = 0 h ∈ S B - - - ( 13 )
Wherein, TkRepresent the no-load voltage ratio of kth transformator, Tk,maxAnd Tk,minRepresent the no-load voltage ratio bound of kth transformator, S respectivelyT Indication transformer set;BhRepresent the susceptance of the h capacitive reactance device, Bh,maxAnd Bh,minRepresent respectively on the susceptance of the h capacitive reactance device Lower limit, SBRepresent capacitive reactance device set;
Step 3-4: solve idle work optimization model, specifically include:
Step 1): initialization vector l, z, u, w, y, each vector kind element is respectively 0.5 ,-0.2,0.5,0.2 ,-0.01, Initializing centripetal parameter Sigma is 0.99;
Step 2): calculate Cgap、Lx、Ly、Lz、Lw、Ll、LuIf, the C calculatedgap、Lx、Ly、Lz、Lw、 Ll、LuIt is respectively less than computational accuracy ε, then stops calculating;
Step 3): according to the C obtainedgapCalculation perturbation variable
Step 4): material calculation coefficient stepPAnd stepD, have:
step P = m i n { m i n i ( - l i &Delta;l i : &Delta;l i < 0 ; - u i &Delta;u i : &Delta;u i < 0 ) } - - - ( 14 )
step D = m i n { m i n i ( - z i &Delta;z i : &Delta;z i < 0 ; - w i &Delta;w i : &Delta;w i < 0 ) } - - - ( 15 )
Step 5): according to stepPAnd stepDRevise x, l, u, y, z, w, have:
x l u = x l u + step P * &Delta; x &Delta; l &Delta; u - - - ( 16 )
y z w = y z w + step D * &Delta; y &Delta; z &Delta; w - - - ( 17 )
Wherein, Δ x, Δ l, Δ u, Δ y, Δ z, Δ w represent the iteration step length of vector x, l, u, y, z, w respectively;
Step 6): revise T by solving equation formula (13)kAnd Bh, have:
Tk=Tk+ΔTk (18)
Bh=Bh+ΔBh (19)
Wherein, Δ TkWith Δ BhFor revising step-length;
Step 7): by revised Tk、Bh, after x, l, u, y, z, w bring equation (12) and (13) into, return step Rapid 2).
Compared with prior art, the beneficial effects of the present invention is:
1) it is the feature of soft-constraint according to voltage in actual motion, uses the method for relaxing of voltage to improve idle work optimization calculating side The convergence of method;
2) it is converted into equality constraint by discrete device is regulated constraint, improves the efficiency that single optimizes, it is possible to adapt to bulk power grid In the optimization analysis that controls of a large amount of discrete device, and propose corresponding optimization method for equality constraint;
3) by by LijIndex converts Pj(R+X)+Qj(X-R) form, under conditions of for increasing model nonconvex property, has pin Property is improved the voltage stability that voltage stability margin is low, thus reaches to improve the purpose of system voltage stability.
Accompanying drawing explanation
Fig. 1 is the idle work optimization method flow chart adapting to bulk power grid automatism voltage control in the embodiment of the present invention.
Detailed description of the invention
Below in conjunction with the accompanying drawings the present invention is described in further detail.
Traditional nonlinear interior-point method calculates idle work optimization and easily occurs owing to what data reasons caused does not restrains, for discrete device Need the most regular or use intelligent algorithm to cause calculating inaccuracy, for considering this three classes situation of voltage stability of system.This Inventing by mathematical distortions and consider voltage operation characteristic, comparing traditional nonlinear interior-point method idle work optimization, the application is according to reality During border is run, voltage is the feature of soft-constraint, uses the method for relaxing of voltage to improve the convergence of idle work optimization computational methods; It is converted into equality constraint by discrete device is regulated constraint, improves the efficiency that single optimizes, it is possible to adapt in bulk power grid is big The optimization analysis that amount discrete device controls, and propose corresponding optimization method for equality constraint;By by LijIndex converts Pj(R+X)+Qj(X-R) form, under conditions of for increasing model nonconvex property, improves voltage stability margin targetedly Low voltage stability, thus reach to improve the purpose of system voltage stability.
Such as Fig. 1, the present invention provides a kind of idle work optimization method adapting to bulk power grid automatism voltage control, and described method includes following Step:
Step 1: determine the voltage stability index of branch road;
Step 2: set up idle work optimization model;
Step 3: use interior point method to solve idle work optimization model.
Described step 1 specifically includes following steps:
Step 1-1: calculate the voltage stability margin L of branch road ij between node i and node jij, the voltage as branch road ij is steady Determine index;
Step 1-2: judge LijWhether exceeding threshold value T, if exceeding, respective branch being contributed to set of fingers M.
In described step 1-1, between node i and node j, the voltage stability margin of branch road ij is LijIt is expressed as:
L i j = 4 &lsqb; 1 - 0.5 B ( X - R ) &rsqb; &lsqb; P j ( X + R ) + Q j ( X - R ) &rsqb; U i 2 ( 1 + sin&delta; i j ) - - - ( 1 )
Wherein, R and X represents resistance and the reactance of branch road ij, δijRepresent the phase difference of voltage of node i and node j, UiRepresent The voltage magnitude of node i, PjAnd QjRepresent outflow active power and the reactive power of node j respectively;
Certain actual electric network result of calculation such as table 1:
Table 1
Circuit name Voltage stability index (threshold value is set to 0.6)
Mountain yellow line 0.650653
Other white line 0.469824
Platform tower line 0.397849
Crow multi-color cord 0.396
Xu Lu line 0.380926
In described step 2, idle work optimization model includes idle work optimization object function and idle work optimization constraints.
Described idle work optimization constraints includes equality constraint and inequality constraints;
Described equality constraint includes trend equality constraint, transformer voltage ratio equality constraint and capacitive reactance device equality constraint;
Described inequality constraints includes that node voltage inequality constraints, voltage slack inequality constraints and generator reactive are exerted oneself not Equality constraint.
Described idle work optimization object function is expressed as:
min f ( x ) = &Sigma; ( i , j ) &Element; M G i j ( U i 2 + U j 2 - 2 U i U j cos&delta; i j ) + &omega; &Sigma; i = 1 N S i 2 + &psi; &Sigma; m &Element; M L i j m - - - ( 2 )
Wherein, f (x) represents idle work optimization object function, and M represents set of fingers, UiAnd UjRepresent node i and node j respectively Voltage magnitude, GijRepresent the conductance of branch road ij, δijRepresenting the phase difference of voltage of node i and node j, N represents node set, M represents that voltage stability margin exceedes the branch road of threshold value;SiRepresent the voltage slack of node i,Represent the voltage of branch road ij Stability margin, ω represents variation weight, and ψ represents voltage stability index weight.
In described equality constraint, have:
(1) trend equality constraint is expressed as:
P G , i - P D , i - U i &Sigma;U j ( G i j cos&delta; i j + B i j sin&delta; i j ) = 0 i &Element; N Q G , i - Q D , i - U i &Sigma;U j ( G i j sin&delta; i j + B i j cos&delta; i j ) = 0 i &Element; N - - - ( 3 )
Wherein, PG,iAnd QG,iRepresent that at node i, electromotor injects active power and reactive power, P respectivelyD,iAnd QD,iRepresent respectively Generated power load and load or burden without work, U at node iiAnd UjRepresent node i and the voltage magnitude of node j, G respectivelyijAnd BijPoint Not Biao Shi the conductance of branch road ij and susceptance, N represents node set, δijFor the phase difference of voltage of node i Yu node j, and δijij, Wherein θi、θjIt is respectively node i, the voltage phase angle of j;
(2) transformer voltage ratio equality constraint is expressed as:
(Tk-Tk,min)(Tk,max-Tk)=0 k ∈ ST (4)
Wherein, TkRepresent the no-load voltage ratio of kth transformator, Tk,maxAnd Tk,minRepresent the no-load voltage ratio bound of kth transformator, S respectivelyT Indication transformer set;
(3) capacitive reactance device equality constraint is expressed as:
(Bh-Bh,min)(Bh,max-Bh)=0 h ∈ SB (5)
Wherein, BhRepresent the susceptance of the h capacitive reactance device, Bh,maxAnd Bh,minRepresent the susceptance bound of the h capacitive reactance device respectively, SBRepresent capacitive reactance device set.
In described inequality constraints, have:
(1) node voltage inequality constraints is expressed as:
Ui,min+Si≤Ui≤Ui,max-Si i∈N (7)
Wherein, SiRepresent the voltage slack of node i, UiRepresent the voltage magnitude of node i, Ui,maxAnd Ui,minRepresent joint respectively The voltage magnitude bound of some i, N represents node set;
(2) inequality constraints of voltage slack is expressed as:
Si≥0 i∈N (8)
Wherein, SiRepresenting the voltage slack of node i, N represents node set;
(3) generator reactive inequality constraints of exerting oneself is expressed as:
QGi,min≤QG,i≤QGi,max i∈N (9)
Wherein, QG,iRepresent that at node i, electromotor injects reactive power, Q respectivelyGi,maxAnd QGi,minRepresent respectively and generate electricity at node i Machine injects reactive power bound, and N represents node set.
Described step 3 specifically includes following steps:
Step 3-1: first idle work optimization model is divided into discrete device equality constraint and continuous quantity Optimized model;
Step 3-2: continuous quantity Optimized model is expressed as:
min f ( x ) = &Sigma; ( i , j ) &Element; M G i j ( U i 2 + U j 2 - 2 U i U j cos&delta; i j ) + &omega; &Sigma; i = 1 N S i 2 + &psi; &Sigma; m &Element; M L i j m &Delta;P i = P G , i - P D , i - U i T k , i &Sigma;U j ( G i j cos&delta; i j + B i j sin&delta; i j ) = 0 , i &Element; N &Delta;Q i = Q G , i + B h , i U i 2 - Q D , i - U i T k , i &Sigma;U j ( G i j sin&delta; i j - B i j cos&delta; i j ) = 0 , i &Element; N U i , min + S i &le; U i &le; U i , max - S i , i &Element; N S i &GreaterEqual; 0 , i &Element; N Q G i , min &le; Q G , i &le; Q G i , max , i &Element; N - - - ( 10 )
Wherein, f (x) represents idle work optimization object function, and M represents set of fingers, UiAnd UjRepresent node i and node j respectively Voltage magnitude, GijRepresent the conductance of branch road ij, δijRepresenting the phase difference of voltage of node i and node j, N represents node set, M represents that voltage stability margin exceedes the branch road of threshold value;SiRepresent the voltage slack of node i,Represent the voltage of branch road ij Stability margin, ω represents variation weight, and ψ represents voltage stability index weight, Bh,iRepresent the h capacitive reactance device at node i Susceptance, Tk,iRepresent the no-load voltage ratio of kth transformator, Δ P at node ii、ΔQiRepresent the deviation and idle of gaining merit at node i respectively Deviation;
Definition vector x=[QG,1,…,QG,i,…,QG,N,S1,…,Si,…,SN,U1,…,Ui,…,UN1,…,θi,…,θN]T, for continuous quantity Optimized model forms unconfined majorized function L, has:
L = f ( x ) - &Sigma; i &Element; N y p i &Delta;P i - &Sigma; i &Element; N y q i &Delta;Q i - &Sigma; i &Element; N z i ( U i - U i , min - S i - l i ) - &Sigma; i &Element; N w i ( U i - U i , max + S i + u i ) - &Sigma; i &Element; S G z i ( Q G , i - U i , min - l i ) - &Sigma; i &Element; S G w i ( U i - U i , max + u i ) - &mu; &Sigma; i &Element; ( N + S G ) ln ( l i ) - &mu; &Sigma; i &Element; ( N + S G ) ln ( u i ) - - - ( 11 )
Wherein, SGRepresenting electromotor node, μ represents disturbance variable, and μ >=0;li、uiRepresent respectively under the voltage of node i Slack variable in slack variable and voltage, ypi、yqi、zi、wiRepresent the lagrange's variable of node i, definition vector L=[l1,l2,……,lr], u=[u1,u2,……,ur], vector y={yp1,…ypi,…,ypN,yq1,…,yqi,…,yqN, vector Z=[z1,z2,……,zr], vector w=[w1,w2,……,wr], r represents inequality number;
Then meet:
L x = &dtri; x f ( x ) - &dtri; x h ( x ) y - &dtri; x g ( x ) ( z + w ) = 0 L y = h ( x ) = 0 L z = g ( x ) - l - g &OverBar; = 0 L w = g ( x ) + u - g &OverBar; = 0 L l = L Z E + &mu; E = 0 L u = U W E - &mu; E = 0 - - - ( 12 )
Wherein, LxRepresent the majorized function L local derviation to vector x, LyRepresent the majorized function L local derviation to vector y, LzRepresent The majorized function L local derviation to vector z, LwRepresent the majorized function L local derviation to vector w, LlRepresent that majorized function L is to vector The local derviation of l, LuRepresent the majorized function L local derviation to vector u,xRepresent idle work optimization object function f (x) inclined to vector x Lead, trend equality constraint vector h (x)={ Δ P1,…,ΔPi,…,ΔPN, Δ Q1,…,ΔQi,…,ΔQN, g (x) represents inequality about Shu Xiangliang,Represent the inequality constraints upper limit,gRepresenting inequality constraints lower limit, L, Z, U, W are respectively li、zi、ui、wi The r of composition ties up diagonal matrix, and the r that E is ties up unit matrix;
Step 3-3: described discrete device equality constraint includes transformer voltage ratio equality constraint and capacitive reactance device equality constraint;
Increase duality gapThen have:
T k ( T k - T k , min ) ( T k , max - T k ) - C g a p = 0 k &Element; S T B h ( B h - B h , min ) ( B h , max - B h ) - C g a p = 0 h &Element; S B - - - ( 13 )
Wherein, TkRepresent the no-load voltage ratio of kth transformator, Tk,maxAnd Tk,minRepresent the no-load voltage ratio bound of kth transformator, S respectivelyT Indication transformer set;BhRepresent the susceptance of the h capacitive reactance device, Bh,maxAnd Bh,minRepresent respectively on the susceptance of the h capacitive reactance device Lower limit, SBRepresent capacitive reactance device set;
Step 3-4: solve idle work optimization model, specifically include:
Step 1): initialization vector l, z, u, w, y, each vector kind element is respectively 0.5 ,-0.2,0.5,0.2 ,-0.01, Initializing centripetal parameter Sigma is 0.99;
Step 2): calculate Cgap、Lx、Ly、Lz、Lw、Ll、LuIf, the C calculatedgap、Lx、Ly、Lz、Lw、 Ll、LuIt is respectively less than computational accuracy ε, then stops calculating;
Step 3): according to the C obtainedgapCalculation perturbation variable
Step 4): material calculation coefficient stepPAnd stepD, have:
step P = m i n { m i n i ( - l i &Delta;l i : &Delta;l i < 0 ; - u i &Delta;u i : &Delta;u i < 0 ) } - - - ( 14 )
step D = m i n { m i n i ( - z i &Delta;z i : &Delta;z i < 0 ; - w i &Delta;w i : &Delta;w i < 0 ) } - - - ( 15 )
Step 5): according to stepPAnd stepDRevise x, l, u, y, z, w, have:
x l u = x l u + step P * &Delta; x &Delta; l &Delta; u - - - ( 16 )
y z w = y z w + step D * &Delta; y &Delta; z &Delta; w - - - ( 17 )
Wherein, Δ x, Δ l, Δ u, Δ y, Δ z, Δ w represent the iteration step length of vector x, l, u, y, z, w respectively;
Step 6): revise T by solving equation formula (13)kAnd Bh, have:
Tk=Tk+ΔTk (18)
Bh=Bh+ΔBh (19)
Wherein, Δ TkWith Δ BhFor revising step-length;
Step 7): by revised Tk、Bh, after x, l, u, y, z, w bring equation (12) and (13) into, return step Rapid 2).
The present invention to voltage, the Volume control of reactive apparatus, uses laxization method to improve this category according to power system Convergence.Secondly as some area discrete device is a lot, and being main regulation equipment, the present invention is by discrete device control Model uses the mode of Constraints to introduce idle work optimization model, although add the convergence number of times that single optimization is analyzed, but can Once calculate to calculate to be converted into by traditional two the most regular suboptimization.Again, for electrical network exists asking of voltage stabilization Topic, and owing to Voltage-stabilizing Problems is generally of locality, utilize and analyze branch voltage steady stability index, by The branch voltage stability index numerical value reducing certain region in Optimized model object function targetedly is steady to the voltage improving this region Determine nargin.
Finally should be noted that: above example only in order to illustrate that technical scheme is not intended to limit, art Those of ordinary skill still the detailed description of the invention of the present invention can be modified or equivalent with reference to above-described embodiment, These are without departing from any amendment of spirit and scope of the invention or equivalent, the claim of the present invention all awaited the reply in application Within protection domain.

Claims (9)

1. the idle work optimization method adapting to bulk power grid automatism voltage control, it is characterised in that: said method comprising the steps of:
Step 1: determine the voltage stability index of branch road;
Step 2: set up idle work optimization model;
Step 3: use interior point method to solve idle work optimization model.
The idle work optimization method of adaptation bulk power grid automatism voltage control the most according to claim 1, it is characterised in that: described Step 1 specifically includes following steps:
Step 1-1: calculate the voltage stability margin L of branch road ij between node i and node jij, the voltage as branch road ij is steady Determine index;
Step 1-2: judge LijWhether exceeding threshold value T, if exceeding, respective branch being contributed to set of fingers M.
The idle work optimization method of adaptation bulk power grid automatism voltage control the most according to claim 2, it is characterised in that: described In step 1-1, between node i and node j, the voltage stability margin of branch road ij is LijIt is expressed as:
L i j = 4 &lsqb; 1 - 0.5 B ( X - R ) &rsqb; &lsqb; P j ( X + R ) + Q j ( X - R ) &rsqb; U i 2 ( 1 + sin&delta; i j ) - - - ( 1 )
Wherein, R and X represents resistance and the reactance of branch road ij, δijRepresent the phase difference of voltage of node i and node j, UiRepresent The voltage magnitude of node i, PjAnd QjRepresent outflow active power and the reactive power of node j respectively.
The idle work optimization method of adaptation bulk power grid automatism voltage control the most according to claim 1, it is characterised in that: described In step 2, idle work optimization model includes idle work optimization object function and idle work optimization constraints.
The idle work optimization method of adaptation bulk power grid automatism voltage control the most according to claim 4, it is characterised in that: described Idle work optimization constraints includes equality constraint and inequality constraints;
Described equality constraint includes trend equality constraint, transformer voltage ratio equality constraint and capacitive reactance device equality constraint;
Described inequality constraints includes that node voltage inequality constraints, voltage slack inequality constraints and generator reactive are exerted oneself not Equality constraint.
The idle work optimization method of adaptation bulk power grid automatism voltage control the most according to claim 4, it is characterised in that: described Idle work optimization object function is expressed as:
min f ( x ) = &Sigma; ( i , j ) &Element; M G i j ( U i 2 + U j 2 - 2 U i U j cos&delta; i j ) + &omega; &Sigma; i = 1 N S i 2 + &psi; &Sigma; m &Element; M L i j m - - - ( 2 )
Wherein, f (x) represents idle work optimization object function, and M represents set of fingers, UiAnd UjRepresent node i and node j respectively Voltage magnitude, GijRepresent the conductance of branch road ij, δijRepresenting the phase difference of voltage of node i and node j, N represents node set, M represents that voltage stability margin exceedes the branch road of threshold value;SiRepresent the voltage slack of node i,Represent the voltage of branch road ij Stability margin, ω represents variation weight, and ψ represents voltage stability index weight.
The idle work optimization method of adaptation bulk power grid automatism voltage control the most according to claim 5, it is characterised in that: described In equality constraint, have:
(1) trend equality constraint is expressed as:
P G , i - P D , i - U i &Sigma; U j ( G i j cos&delta; i j + B i j sin&delta; i j ) = 0 i &Element; N P G , i - P D , i - U i &Sigma; U j ( G i j sin&delta; i j - B i j cos&delta; i j ) = 0 i &Element; N - - - ( 3 )
Wherein, PG,iAnd QG,iRepresent that at node i, electromotor injects active power and reactive power, P respectivelyD,iAnd QD,iRepresent respectively Generated power load and load or burden without work, U at node iiAnd UjRepresent node i and the voltage magnitude of node j, G respectivelyijAnd BijPoint Not Biao Shi the conductance of branch road ij and susceptance, N represents node set, δijFor the phase difference of voltage of node i Yu node j, and δijij, Wherein θi、θjIt is respectively node i, the voltage phase angle of j;
(2) transformer voltage ratio equality constraint is expressed as:
(Tk-Tk,min)(Tk,max-Tk)=0 k ∈ ST (4)
Wherein, TkRepresent the no-load voltage ratio of kth transformator, Tk,maxAnd Tk,minRepresent the no-load voltage ratio bound of kth transformator, S respectivelyT Indication transformer set;
(3) capacitive reactance device equality constraint is expressed as:
(Bh-Bh,min)(Bh,max-Bh)=0 h ∈ SB(5)
Wherein, BhRepresent the susceptance of the h capacitive reactance device, Bh,maxAnd Bh,minRepresent the susceptance bound of the h capacitive reactance device respectively, SBRepresent capacitive reactance device set.
The idle work optimization method of adaptation bulk power grid automatism voltage control the most according to claim 5, it is characterised in that: described In inequality constraints, have:
(1) node voltage inequality constraints is expressed as:
Ui,min+Si≤Ui≤Ui,max-Si i∈N (7)
Wherein, SiRepresent the voltage slack of node i, UiRepresent the voltage magnitude of node i, Ui,maxAnd Ui,minRepresent joint respectively The voltage magnitude bound of some i, N represents node set;
(2) inequality constraints of voltage slack is expressed as:
Si≥0 i∈N (8)
Wherein, SiRepresenting the voltage slack of node i, N represents node set;
(3) generator reactive inequality constraints of exerting oneself is expressed as:
QGi,min≤QG,i≤QGi,max i∈N (9)
Wherein, QG,iRepresent that at node i, electromotor injects reactive power, Q respectivelyGi,maxAnd QGi,minRepresent respectively and generate electricity at node i Machine injects reactive power bound, and N represents node set.
The idle work optimization method of adaptation bulk power grid automatism voltage control the most according to claim 1, it is characterised in that: described Step 3 specifically includes following steps:
Step 3-1: first idle work optimization model is divided into discrete device equality constraint and continuous quantity Optimized model;
Step 3-2: continuous quantity Optimized model is expressed as:
{ min f ( x ) = &Sigma; ( i , j ) &Element; M G i j ( U i 2 + U j 2 - 2 U i U j cos&delta; i j ) + &omega; &Sigma; i = 1 N S i 2 + &psi; &Sigma; m &Element; M L i j m &Delta;P i = P G , i - P D , i - U i T k , i &Sigma; U j ( G i j cos&delta; i j + B i j sin&delta; i j ) = 0 i &Element; N &Delta;Q i = Q G , i + B h , i U i 2 - Q D , i - U i T k , i &Sigma; U j ( G i j sin&delta; i j - B i j cos&delta; i j ) = 0 i &Element; N U i , min + S i &le; U i &le; U i , max - S i i &Element; N S i &GreaterEqual; 0 i &Element; N Q G i , min &le; Q G , i &le; Q G i , max i &Element; N - - - ( 10 )
Wherein, f (x) represents idle work optimization object function, and M represents set of fingers, UiAnd UjRepresent node i and node j respectively Voltage magnitude, GijRepresent the conductance of branch road ij, δijRepresenting the phase difference of voltage of node i and node j, N represents node set, M represents that voltage stability margin exceedes the branch road of threshold value;SiRepresent the voltage slack of node i,Represent the voltage of branch road ij Stability margin, ω represents variation weight, and ψ represents voltage stability index weight, Bh,iRepresent the h capacitive reactance device at node i Susceptance, Tk,iRepresent the no-load voltage ratio of kth transformator, Δ P at node ii、ΔQiRepresent the deviation and idle of gaining merit at node i respectively Deviation;
Definition vector x=[QG,1,…,QG,i,…,QG,N,S1,…,Si,…,SN,U1,…,Ui,…,UN1,…,θi,…,θN]T, for continuous quantity Optimized model forms unconfined majorized function L, has:
L = f ( x ) - &Sigma; i &Element; N y p i &Delta;P i - &Sigma; i &Element; N y q i &Delta;Q i - &Sigma; i &Element; N z i ( U i - U i , min - S i - l i ) - &Sigma; i &Element; N w i ( U i - U i , max + S i + u i ) - &Sigma; i &Element; S G z i ( Q G , i - U i , min - l i ) - &Sigma; i &Element; S G w i ( U i - U i , max + u i ) - &mu; &Sigma; i &Element; ( N + S G ) ln ( l i ) - &mu; &Sigma; i &Element; ( N + S G ) ln ( u i ) - - - ( 11 )
Wherein, SGRepresenting electromotor node, μ represents disturbance variable, and μ >=0;li、uiRepresent respectively under the voltage of node i Slack variable in slack variable and voltage, ypi、yqi、zi、wiRepresent the lagrange's variable of node i, definition vector L=[l1,l2,……,lr], u=[u1,u2,……,ur], vector y={yp1,…ypi,…,ypN,yq1,…,yqi,…,yqN, vector Z=[z1,z2,……,zr], vector w=[w1,w2,……,wr], r represents inequality number;
Then meet:
L x = &dtri; x f ( x ) - &dtri; x h ( x ) y - &dtri; x g ( x ) ( z + w ) = 0 L y = h ( x ) = 0 L w = g ( x ) - l - g &OverBar; = 0 L w = g ( x ) + u - g &OverBar; = 0 L l = L Z E + &mu; E = 0 L u = U W E - &mu; E = 0 - - - ( 12 )
Wherein, LxRepresent the majorized function L local derviation to vector x, LyRepresent the majorized function L local derviation to vector y, LzRepresent The majorized function L local derviation to vector z, LwRepresent the majorized function L local derviation to vector w, LlRepresent that majorized function L is to vector The local derviation of l, LuRepresent the majorized function L local derviation to vector u,xRepresent idle work optimization object function f (x) inclined to vector x Lead, trend equality constraint vector h (x)={ Δ P1,…,ΔPi,…,ΔPN, Δ Q1,…,ΔQi,…,ΔQN, g (x) represents inequality about Shu Xiangliang,Represent the inequality constraints upper limit,gRepresenting inequality constraints lower limit, L, Z, U, W are respectively li、zi、ui、wi The r of composition ties up diagonal matrix, and the r that E is ties up unit matrix;
Step 3-3: described discrete device equality constraint includes transformer voltage ratio equality constraint and capacitive reactance device equality constraint;
Increase duality gap C g a p = &Sigma; i = 1 r ( u i w i - l i z i ) , Then have:
T k ( T k - T k , min ) ( T k , max - T k ) - C g a p = 0 k &Element; S T B h ( B h - B h , min ) ( B h , max - B h ) - C g a p = 0 h &Element; S B - - - ( 13 )
Wherein, TkRepresent the no-load voltage ratio of kth transformator, Tk,maxAnd Tk,minRepresent the no-load voltage ratio bound of kth transformator, S respectivelyT Indication transformer set;BhRepresent the susceptance of the h capacitive reactance device, Bh,maxAnd Bh,minRepresent respectively on the susceptance of the h capacitive reactance device Lower limit, SBRepresent capacitive reactance device set;
Step 3-4: solve idle work optimization model, specifically include:
Step 1): initialization vector l, z, u, w, y, each vector kind element is respectively 0.5 ,-0.2,0.5,0.2 ,-0.01, Initializing centripetal parameter Sigma is 0.99;
Step 2): calculate Cgap、Lx、Ly、Lz、Lw、Ll、LuIf, the C calculatedgap、Lx、Ly、Lz、Lw、 Ll、LuIt is respectively less than computational accuracy ε, then stops calculating;
Step 3): according to the C obtainedgapCalculation perturbation variable
Step 4): material calculation coefficient stepPAnd stepD, have:
step P = min { min i ( - l i &Delta;l i : &Delta;l i < 0 ; - u i &Delta;u i : &Delta;u i < 0 ) } - - - ( 14 )
step D = m i n { min i ( - z i &Delta;z i : &Delta;z i < 0 ; - w i &Delta;w i : &Delta;w i < 0 ) } - - - ( 15 )
Step 5): according to stepPAnd stepDRevise x, l, u, y, z, w, have:
x l u = x l u + step P * &Delta; x &Delta; l &Delta; u - - - ( 16 )
y z w = y z w + step D * &Delta; y &Delta; z &Delta; w - - - ( 17 )
Wherein, Δ x, Δ l, Δ u, Δ y, Δ z, Δ w represent the iteration step length of vector x, l, u, y, z, w respectively;
Step 6): revise T by solving equation formula (13)kAnd Bh, have:
Tk=Tk+ΔTk (18)
Bh=Bh+ΔBh (19)
Wherein, Δ TkWith Δ BhFor revising step-length;
Step 7): by revised Tk、Bh, after x, l, u, y, z, w bring equation (12) and (13) into, return step Rapid 2).
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