CN105552960A - Voltage stabilization analyzing method and device for power system of wind power plant - Google Patents

Abstract

The embodiment of the invention provides a voltage stabilization analyzing method and device for a power system of a wind power plant. The method comprises: selecting continuous parameters to form a new equation, expanding the flow equation of the power system by using the new equation, correcting the expanded flow equation of the power system to obtain corrected flow equation of the power system, wherein in the corrected flow equation of the power system, the corrected flow jacobian matrix is the flow jacobian matrix generated when the node in the power system with maximum reduced voltage amplitude value is processed as the node with appointed injection power and voltage amplitude value; using a Newton-Raphson algorithm iteration to solve the corrected flow equation of the power system so as to obtain a prediction direction; determining a predication point according to the prediction direction and a preset step size; and analyzing the voltage stabilization condition of the power system of the wind power plant according to the prediction point. According to the scheme of the invention, the convergence of the continuous flow calculation nearby the critical point is greatly improved; and the reliability of the algorithm is greatly improved.

Description

The Voltage Stability Analysis method of wind energy turbine set electric power system and device

Technical field

The present invention relates to power safety technique field, the Voltage Stability Analysis method of particularly a kind of wind energy turbine set electric power system and device.

Background technology

The reactive power characteristic of wind energy turbine set is relevant with the active power characteristic of wind energy turbine set.When the meritorious output of wind energy turbine set is lower, transmission line underloading, surplus that line charging is idle, wind turbine generator answers absorbing reactive power.If the reactive power that wind turbine generator absorbs is not enough, then wind energy turbine set will be injected idle to electrical network, and may occur high voltage problem.And wind energy turbine set is meritorious exports when increasing, transmission line heavy duty, the perception of consumption is idle to be increased thereupon, and line charging is idle, and to be not enough to offset the perception of the components consume such as circuit and main transformer idle, and wind turbine generator should send reactive power.If the reactive power that wind turbine generator sends is not enough, then wind energy turbine set will absorb idle from electrical network.If wind energy turbine set absorbs idle from electrical network, wind energy turbine set Voltage Drop may be caused.Therefore, when electric network reactive-load is not enough, may there is Voltage-stabilizing Problems in meritorious the exerting oneself when sending out greatly or completely send out of Wind turbines, be necessary to carry out detailed Voltage Stability Analysis.

Continuation Method is one of basic skills of Voltage Stability Analysis, by selecting certain serialization parameter to ensure the convergence of critical point and neighbouring Load flow calculation thereof, and introduce the mechanism such as prediction, correction and step-length adjustment, to reduce the iterations needed for computational process as much as possible, reduce amount of calculation.The every bit of its λ – V curve all iterates, and calculates trend accurately, so can obtain the information such as λ – V curve accurately, and can consider certain nonlinear Control and inequality constraints condition, have stronger robustness.

Existing Continuation Method is generally increase an equation on continuous tide fundamental equation basis, λ is used as variable simultaneously, thus makes the lower right of Jacobian matrix add lastrow one row, even if the Jacobian matrix after expansion remains good state in critical point place; But, its upper left hand corner section is but still unusual in critical point place, therefore continuous tide calculates and is difficult to effectively be ensured in the convergence of Near The Critical Point, the reliability of algorithm is a greater impact, and then has influence on the reliability of Voltage Stability Analysis of wind energy turbine set electric power system.

Summary of the invention

Embodiments provide a kind of Voltage Stability Analysis method of wind energy turbine set electric power system, with solve continuous tide in prior art calculate be difficult to effectively to be ensured in the convergence of Near The Critical Point, technical problem that the reliability of algorithm is a greater impact.The method comprises: select serialization parameter to form new equation, utilize the power flow equation of described new equation extended power system, the power flow equation of the electric power system after expansion is revised, obtain the power flow equation of revised electric power system, in the power flow equation of revised electric power system, revised Load Flow Jacobian Matrix is the Load Flow Jacobian Matrix of maximum node when being used as the node processing that injecting power and voltage magnitude all specify that declined by voltage magnitude in electric power system; Adopt the power flow equation of revised electric power system described in Newton-Raphson approach iterative, obtain prediction direction; According to described prediction direction and default step-length, determine future position; The voltage stabilization situation of wind energy turbine set electric power system is analyzed according to described future position.

In one embodiment, the power flow equation of described revised electric power system is:

$J^{\′\′}\left[\begin{array}{c}\mathrm{\Δ}{x}^{\′}\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=-\left[\begin{array}{c}{f}^{\′}\left(x\right)+{\mathrm{\λb}}^{\′}\\ f_k\left(x\right)+{\mathrm{\λb}}_k\end{array}\right]$

Wherein, x is state vector; F (x) is trend equilibrium equation, and k is line number; $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ J " is the Jacobian matrix of revised extended power flow equations; F ' _xit is revised Load Flow Jacobian Matrix; B ' is revised load growth direction; b _kfor a kth element of b; X ' is revised state vector; F ' (x) is revised power flow equation group; f _kan x kth element that () is vector function f (x); f _{kx '}for function f _kx () is to the gradient vector of x '; Δ x ' is the change vector corresponding with x ', and Δ λ is the variable quantity of the horizontal λ of wind power output.

In one embodiment, adopt the power flow equation of revised electric power system described in Newton-Raphson approach iterative, comprise: when after previous Load flow calculation, by the trend solution of following formula predictions Load flow calculation next time, and using the initial value of the trend solution of prediction as Load flow calculation next time:

$\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=\left[\begin{array}{c}0\\ -1\end{array}\right]$

Wherein, t _kbe a kth element be 1, all the other elements are the column vector of 0; B is load growth direction; f _xit is the Jacobian matrix of the power flow equation of electric power system; Δ λ is the variable quantity of the horizontal λ of wind power output, and Δ x is state variation vector, Δ x _kthe row k element of Δ x, by Δ x _kbe used as constant.

In one embodiment, the step-length by presetting described in following formulae discovery:

$h=h_{max}/\underset{i=1}{\overset{n}{\max }}\left(y_i\right)$

Wherein, h is default step-length; h _maxfor constant; y _ifor i-th component of prediction direction y, n is positive integer.

The embodiment of the present invention additionally provides a kind of Voltage Stability Analysis device of wind energy turbine set electric power system, with solve continuous tide in prior art calculate be difficult to effectively to be ensured in the convergence of Near The Critical Point, technical problem that the reliability of algorithm is a greater impact.This device comprises: equation expansion correcting module, new equation is formed for selecting serialization parameter, utilize the power flow equation of described new equation extended power system, the power flow equation of the electric power system after expansion is revised, obtain the power flow equation of revised electric power system, in the power flow equation of revised electric power system, revised Load Flow Jacobian Matrix is the Load Flow Jacobian Matrix of maximum node when being used as the node processing that injecting power and voltage magnitude all specify that declined by voltage magnitude in electric power system; Solving module, for adopting the power flow equation of revised electric power system described in Newton-Raphson approach iterative, obtaining prediction direction; Determination module, for according to described prediction direction and default step-length, determines future position; Analysis module, for analyzing the voltage stabilization situation of wind energy turbine set electric power system according to described future position.

In one embodiment, the power flow equation of described revised electric power system is:

$J^{\′\′}\left[\begin{array}{c}\mathrm{\Δ}{x}^{\′}\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=-\left[\begin{array}{c}{f}^{\′}\left(x\right)+{\mathrm{\λb}}^{\′}\\ f_k\left(x\right)+{\mathrm{\λb}}_k\end{array}\right]$

Wherein, x is state vector, and f (x) is trend equilibrium equation, and k is line number; $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ J " is the Jacobian matrix of the power flow equation of the electric power system of revised expansion; F ' _xit is revised Load Flow Jacobian Matrix; B ' is revised load growth direction b; b _kfor a kth element of b; X ' is revised vector; F ' (x) is revised power flow equation group; f _kan x kth element that () is vector function f (x); f _{kx '}for function f _kx () is to the gradient vector of x '; Δ x ' is the change vector corresponding with x ', and Δ λ is the variable quantity of the horizontal λ of wind power output.

In one embodiment, module is solved, specifically for when after previous Load flow calculation, by the trend solution of following formula predictions Load flow calculation next time, and using the initial value of the trend solution of prediction as Load flow calculation next time described in:

$\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=\left[\begin{array}{c}0\\ -1\end{array}\right]$

Wherein, t _kbe a kth element be 1, all the other elements are the column vector of 0; B is load growth direction; f _xit is the Jacobian matrix of the power flow equation of electric power system; Δ λ is the variable quantity of the horizontal λ of wind power output; Δ x is state variation vector; Δ x _kthe row k element of Δ x, by Δ x _kbe used as constant.

In one embodiment, also comprise: step size computation module, the step-length for by presetting described in following formulae discovery:

$h=h_{max}/\underset{i=1}{\overset{n}{\max }}\left(y_i\right)$

Wherein, h is default step-length; h _maxfor constant; y _ifor i-th component of prediction direction y, n is positive integer.

In embodiments of the present invention, by the power flow equation utilizing new equation to carry out extended power system, the power flow equation after expanding is made to be the equation can trying to achieve definite value solution, and by revising the power flow equation of the electric power system after expansion, revised Load Flow Jacobian Matrix is made to be weak node most in electric power system (i.e. voltage magnitude decline maximum node) is used as Load Flow Jacobian Matrix when PV node (i.e. injecting power and voltage magnitude all specify node) processes, namely the power flow equation of revised electric power system Jacobian matrix critical point and near be nonsingular, and amended Load Flow Jacobian Matrix (i.e. the Jacobian matrix left sub matrix of the power flow equation of revised electric power system) critical point and near be also nonsingular, solve the singular problem of expansion Load Flow Jacobian Matrix left sub matrix (i.e. Load Flow Jacobian Matrix) critical point place, overcome the harmful effect that the unusual and neighbouring morbid state of Load Flow Jacobian Matrix critical point place is brought to numerical computations, the computational accuracy of expansion update equation can effectively be ensured, continuous tide calculates and greatly improves in the convergence of Near The Critical Point, add the reliability of algorithm.

Accompanying drawing explanation

Accompanying drawing described herein is used to provide a further understanding of the present invention, forms a application's part, does not form limitation of the invention.In the accompanying drawings:

Fig. 1 is the flow chart of the Voltage Stability Analysis method of a kind of wind energy turbine set electric power system that the embodiment of the present invention provides;

Fig. 2 is the explanation schematic diagram of a kind of point-by-point method that the embodiment of the present invention provides;

Fig. 3 is the explanation schematic diagram of a kind of arc length continuity method that the embodiment of the present invention provides;

Fig. 4 is the explanation schematic diagram of a kind of same year community that the embodiment of the present invention provides;

Fig. 5 is the explanation schematic diagram of a kind of local parameter continuity method that the embodiment of the present invention provides;

A kind of one of λ – V curve synoptic diagram when considering idle restriction that Fig. 6 is that the embodiment of the present invention provides;

A kind of λ – V curve synoptic diagram two when considering idle restriction that Fig. 7 is that the embodiment of the present invention provides;

A kind of λ – V curve synoptic diagram three when considering idle restriction that Fig. 8 is that the embodiment of the present invention provides;

Fig. 9 is the structured flowchart of the Voltage Stability Analysis device of a kind of wind energy turbine set electric power system that the embodiment of the present invention provides.

Embodiment

For making the object, technical solutions and advantages of the present invention clearly understand, below in conjunction with execution mode and accompanying drawing, the present invention is described in further details.At this, exemplary embodiment of the present invention and illustrating for explaining the present invention, but not as a limitation of the invention.

In embodiments of the present invention, provide a kind of Voltage Stability Analysis method of wind energy turbine set electric power system, as shown in Figure 1, the method comprises:

Step 101: select serialization parameter to form new equation, utilize the power flow equation of described new equation extended power system, the power flow equation of the electric power system after expansion is revised, obtain the power flow equation of revised electric power system, in the power flow equation of revised electric power system, revised Load Flow Jacobian Matrix is the Load Flow Jacobian Matrix of maximum node when being used as the node processing that injecting power and voltage magnitude all specify that declined by voltage magnitude in electric power system;

Step 102: the power flow equation adopting revised electric power system described in Newton-Raphson approach iterative, obtains prediction direction;

Step 103: according to described prediction direction and default step-length, determine future position;

Step 104: the voltage stabilization situation analyzing wind energy turbine set electric power system according to described future position.

Flow process is as shown in Figure 1 known, in embodiments of the present invention, by the power flow equation utilizing new equation to carry out extended power system, the power flow equation after expanding is made to be the equation can trying to achieve definite value solution, and by revising the power flow equation of the electric power system after expansion, revised Load Flow Jacobian Matrix is made to be weak node most in electric power system (i.e. voltage magnitude decline maximum node) is used as Load Flow Jacobian Matrix when PV node (i.e. injecting power and voltage magnitude all specify node) processes, namely the power flow equation of revised electric power system Jacobian matrix critical point and near be nonsingular, and amended Load Flow Jacobian Matrix (i.e. the Jacobian matrix left sub matrix of the power flow equation of revised electric power system) critical point and near be also nonsingular, solve the singular problem of expansion Load Flow Jacobian Matrix left sub matrix (i.e. Load Flow Jacobian Matrix) critical point place, overcome the harmful effect that the unusual and neighbouring morbid state of Load Flow Jacobian Matrix critical point place is brought to numerical computations, the computational accuracy of expansion update equation can effectively be ensured, continuous tide calculates and greatly improves in the convergence of Near The Critical Point, add the reliability of algorithm.

During concrete enforcement, because the power flow equation by the electric power system after above-mentioned new equation expansion is the equation can trying to achieve definite value solution, and expansion after Jacobian matrix nonsingular in critical point place, but the left sub matrix (i.e. conventional Load Flow Jacobian matrix) of the Jacobian matrix after expansion is unusual in critical point place, Near The Critical Point morbid state, make expand after power flow equation critical point and near computational accuracy be difficult to effectively be ensured, Continuation Method critical point and near convergence will cannot effectively be ensured equally, therefore, in order to the left sub matrix (i.e. conventional Load Flow Jacobian matrix) realizing the Jacobian matrix after expanding is nonsingular in critical point place, in the present embodiment, the power flow equation of the electric power system after expansion is revised, the power flow equation obtaining revised electric power system is:

$J^{\′\′}\left[\begin{array}{c}\mathrm{\Δ}{x}^{\′}\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=-\left[\begin{array}{c}{f}^{\′}\left(x\right)+{\mathrm{\λb}}^{\′}\\ f_k\left(x\right)+{\mathrm{\λb}}_k\end{array}\right]$

Wherein, x is state vector, the vector be namely made up of voltage magnitude and the phase place of each node; F (x) is trend equilibrium equation, and k is line number; $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ J " is the Jacobian matrix of the power flow equation of the electric power system of revised expansion; F ' _xrevised Load Flow Jacobian Matrix, namely Load Flow Jacobian Matrix scratch row k and kth row after residual matrix; B ' is revised load growth direction b, and namely b scratches the residual vector after row k; b _kfor a kth element of b; X ' is revised vector x, and namely x scratches the residual vector after row k; F ' (x) is revised power flow equation group, and namely functional vector f (x) scratches the residual vector after row k; f _kan x kth element that () is vector function f (x); f _{kx '}for function f _kx () is to the gradient vector of x '; Δ x ' is the change vector corresponding with x ', and Δ λ is the variable quantity of the horizontal λ of wind power output.Concrete, by x _kbe used as constant, and by Equation f _k(x)+λ b _k=0 moves to last column, can find out, J, and " in fact row k is moved on to last column after scratching the (n+1)th row kth row and obtains by J ' (Jacobian matrix of power flow equation of the electric power system namely after expansion), f ' _xfor conventional Load Flow Jacobian matrix f _xscratch the matrix after row k kth row; B ' scratches the vector after a kth element for vectorial b; b _kfor a kth element of vectorial b; X ' scratches the vector after a kth element for vector x; F ' (x) scratches the vector after a kth element for vector function f (x); f _kan x kth element that () is vector function f (x); f _{kx '}for function f _kx () is to the gradient vector of x '.

During concrete enforcement, continuous tide calculates and adopts Newton-Raphson approach de-spread power flow equation.After Load flow calculation each time, if predict trend solution next time, and using the trend solution of prediction as the initial value of Load flow calculation next time, obviously can greatly reduce the iterations of Load flow calculation, accelerate computational speed.In order to improve success rate prediction, the precision improving forecasting process and robustness, in the present embodiment, adopt the power flow equation of revised electric power system described in Newton-Raphson approach iterative, comprise: when after previous Load flow calculation, by the trend solution of following formula predictions Load flow calculation next time, and using the initial value of the trend solution of prediction as Load flow calculation next time:

$\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=\left[\begin{array}{c}0\\ -1\end{array}\right]$

Wherein, t _kbe a kth element be 1, all the other elements are the column vector of 0; B is load growth direction; f _xit is the Jacobian matrix of the power flow equation of electric power system; Δ λ is the variable quantity of the horizontal λ of wind power output, and Δ x is state variation vector, Δ x _kthe row k element of Δ x, by Δ x _kbe used as constant, by Δ x _kbe used as constant, namely scratch formula $\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=\left[\begin{array}{c}0\\ -1\end{array}\right]$ Last column and by f _xkth row move to right-hand vector, then the row k of equation is moved to last column, solve this equation prediction direction y.

During concrete enforcement, after giving prediction direction, also need to provide step-length h, could future position be determined.The performance of selection on Continuation Method of step-length has important impact.Step-length obtains too little, and Load flow calculation can Fast Convergent each time, but will calculate and just can calculate Near The Critical Point many times, and to calculate the lower branch of λ – V curve, then required number of times is more.Step-length obtains too large, and the distance of future position and required point may be comparatively far away, and the iterations each time needed for Load flow calculation is more, and the possibility of result spends more computing time on the contrary, continuous tide even may be caused to calculate and do not restrain.Generally speaking, the basic principle that step-length is selected is that step-length gets higher value in curve more smooth part; The part relatively bent at curve then gets smaller value.Therefore, in the present embodiment, the step-length by presetting described in following formulae discovery:

$h=h_{max}/\underset{i=1}{\overset{n}{\max }}\left(y_i\right)$

Wherein, h is default step-length; h _maxfor constant; y _ifor i-th component of prediction direction y, n is positive integer.Concrete, in continuous tide calculates, also can introduce the concept of variable step, if the iterations needed for the calculating of this continuous tide reduces step-length more at most, iterations increases step-length more at least, and iterations is moderate, keeps former step-length.

The Voltage Stability Analysis method of above-mentioned wind energy turbine set electric power system is described below in conjunction with concrete example.Such as:

The basic power flow equation of electric power system is:

f(x)+λb＝0(1)

Wherein, x ∈ R ⁿ; F (x) is n dimension functional vector; B is load growth direction, b ∈ R ⁿ; λ is argument variable, and from the angle of physics, it represents the load level of system in fact to a certain extent.

The basic power flow equation of formula (1) has n+1 variable, but only has n equation, can not solve definite value solution, and it is actually a curve on n+1 dimension space.For trying to achieve definite value solution, an equation must be increased.The simplest also the most intuitively method yes adopts the point-by-point method shown in Fig. 2, in each Load flow calculation, first determine the value of λ, then can try to achieve corresponding definite value solution.But when λ gets a certain higher value, update equation may occur morbid state, and increase along with the continuation of λ value, its pathosis will be more serious, when λ large to a certain extent time, the morbid state of update equation will make conventional Load Flow calculating to restrain.The point-by-point method key diagram of Fig. 2 intuitively understands this point.Along with increasing the weight of of load level, λ value constantly increases, future position x _pmove right, work as x _pduring x Yu λ – V contact of a curve, x is voltage collapse critical point, but due to Jacobian matrix unusual in critical point place, Near The Critical Point morbid state, Load flow calculation cannot be restrained, numerical computations failure.For overcoming this shortcoming, Continuation Method just arises at the historic moment.

The key of Continuation Method is to select rational serialization parameter to ensure critical point and neighbouring convergence thereof.At present, continuous parameters method mainly contains arc length continuity method, same year community and local continuous parameters method.

Fig. 3 gives the basic conception of arc length continuity method intuitively, and its basic ideas are by introducing parameter S representative from x to initial point x ₀arc length, and get S and equal x ₀x _plength realize, namely newly-increased equation is:

$\underset{i=1}{\overset{n}{\Σ}}{(x_i-x_{i0})}^2+{(\mathrm{\λ}-{\mathrm{\λ}}_0)}^2=S^2---\left(2\right)$

Wherein, $S^2-\underset{i=1}{\overset{n}{\Σ}}{(x_{ip}-x_{i0})}^2+{({\mathrm{\λ}}_p-{\mathrm{\λ}}_0)}^2.$

Fig. 4 gives the basic conception of same year community intuitively, and its basic ideas make vector x-x _pwith vector x ₀-x _pvertically, equation (i.e. above-mentioned new equation) can be increased thus:

$\underset{i=1}{\overset{n}{\Σ}}(x_{ip}-x_{i0})(x_{ip}-x_i)+({\mathrm{\λ}}_{ip}-{\mathrm{\λ}}_0)({\mathrm{\λ}}_{ip}-\mathrm{\λ})=0---\left(3\right)$

Fig. 5 intuitively understands the basic conception of local parameter continuity method.Its basic ideas are then first determine a certain element of vector x according to prediction direction, namely according to x ₀and x _pincrease equation (i.e. above-mentioned new equation):

x _k＝x _pk(4)

Wherein, k is subscript corresponding to local continuous parameter, general amount of orientation x in practicality _p-x ₀the subscript that maximum absolute value element is corresponding, calculates for continuous tide, then k can be defined in the element corresponding to voltage.

Through above-mentioned process, the power flow equation after expansion has n+1 equation, and n+1 variable, can try to achieve definite value solution thus.

For convenience of explanation, equation (i.e. above-mentioned new equation) unification g (x, λ)=0 increased above is represented.With Newton-Raphson approach de-spread power flow equation, then the power flow equation after corresponding expansion is as follows:

$J^{\′}\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=-\left[\begin{array}{c}f\left(x\right)+\mathrm{\λ}b\\ g(x,\mathrm{\λ})\end{array}\right]---\left(5\right)$

Wherein, $J^{\′}=\left[\begin{array}{cc}{f}_x& b\\ t_x^T& g_{\mathrm{\λ}}\end{array}\right],$ J=f _xfor the Jacobian matrix of conventional Load Flow, J ' is the Jacobian matrix of power flow equation after expansion, and subscript T represents transposition.

If critical point is normal flex point (i.e. saddle node bifurcation point), then the Jacobian matrix J ' of extended power flow equations is nonsingular in critical point place.

For solving of formula (5) curved-edge polygons, because expansion Load Flow Jacobian Matrix J ' is nonsingular in critical point place, if triangle decomposition pivoting, the method reliably can calculate voltage collapse critical point.But for openness consideration, general not pivoting during Jacobian matrix triangle decomposition, again due to J ' left sub matrix f _x(i.e. conventional Load Flow Jacobian matrix) is unusual in critical point place, Near The Critical Point morbid state, make curved-edge polygons critical point and near computational accuracy be difficult to effectively be ensured, Continuation Method critical point and near convergence will cannot effectively be ensured equally.

For overcoming above-mentioned shortcoming, the algorithm realization of local continuous parameters method is suitably revised.In iterative λ – V curve and newly-increased EQUATION x _k=x _pkintersection point process in, not by x _k=x _pkbe used as equation to consider, but by x _kbe used as constant, and by Equation f _k(x)+λ b _k=0 moves to last column.Correspondingly, adopt the update equation (i.e. the power flow equation of above-mentioned revised electric power system) corresponding to Newton-Raphson approach iterative as follows:

$J^{\′\′}\left[\begin{array}{c}\mathrm{\Δ}{x}^{\′}\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=-\left[\begin{array}{c}{f}^{\′}\left(x\right)+{\mathrm{\λb}}^{\′}\\ f_k\left(x\right)+{\mathrm{\λb}}_k\end{array}\right]---\left(6\right)$

Wherein, $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ J " is above-mentioned revised Load Flow Jacobian Matrix; F ' _xfor f _xscratch the matrix after row k kth row; B ' scratches the vector after a kth element for vectorial b; b _kfor a kth element of vectorial b; X ' scratches the vector after a kth element for vector x; F ' (x) scratches the vector after a kth element for vector function f (x); f _kan x kth element that () is vector function f (x); f _{kx '}for function f _kx () is to the gradient vector of x '.

Can find out, J that " in fact row k is moved on to last column and obtains after scratching the (n+1)th row kth row by J '.

For local parameter continuity method, in formula (5) now suppose J " unusual in critical point place, then make J " w=0.Construct vectorial w '=(w ₁, w ₂..., w _k-1, 0, w _k..., w _n) ^t, then J ' w '=0 is had.Can w ' ≠ 0 be obtained by w ≠ 0, therefore have J ' unusual.This and the nonsingular contradiction of normal flex point place J ', if namely this demonstrate critical point is normal flex point, J is " nonsingular in critical point place.

For electric power system continuous tide calculate, voltage collapse critical point and near, according to the selection principle of above-mentioned subscript k, x _kshould correspond to the voltage of the fastest node of voltage drop, this shows f ' _xit is Load Flow Jacobian Matrix when most for system weak node being used as PV node processing.From the angle of physics, a certain node is used as PV node processing and in fact means that this node voltage remains constant.Can imagine, if it is constant to maintain this node voltage to drop into sufficient reactive power source at a certain weak node of system, then the voltage stability margin of system will increase, and this just means f ' _xcritical point place is nonsingular.As can be seen here, even if in critical point place, f ' _xand J " all nonsingular, Continuation Method reliably can calculate voltage collapse critical point.

From the angle of interspace analytic geometry, the every bit that continuous tide calculates is equivalent to the intersection point of Qiu λ – V curve and the space curved surface corresponding to newly-increased equation.With the intersection point of a curve and a curved surface in Newton-Raphson approach iterative hyperspace, when this curve and surface is tangent, corresponding Jacobian matrix is unusual, and numerical computations cannot restrain, time orthogonal, its convergence then should be best, and when intersecting, its convergence falls between.Power flow equation Jacobian matrix critical point place unusual is just deriving from the tangent of λ – V curve and the constant curved surface of λ.For Continuation Method, the space curved surface corresponding due to newly-increased equation is no longer tangent but crossing Yu λ – V curve, thus makes the Load Flow Jacobian Matrix of expansion no longer unusual.

The morbid state of the left sub matrix of the expansion Load Flow Jacobian Matrix caused because conventional Load Flow Jacobian matrix Near The Critical Point is ill was not all solved due to former Continuation Method, thus causing expansion update equation to be affected in the computational accuracy of Near The Critical Point, the convergence that continuous tide calculates cannot effectively be ensured.Adopt this method, owing to solving the unusual of expansion Load Flow Jacobian Matrix upper left hand corner section critical point place, the computational accuracy of expansion update equation can effectively be ensured, continuous tide calculates and greatly improves in the convergence of Near The Critical Point.In fact, for two-dimentional system, local parameter continuity method increases space curved surface corresponding to equation newly at critical point place Yu λ – V orthogonal curve, and pass through the improvement of this project, the computational accuracy of expansion update equation can effectively be ensured again, and the convergence of its Near The Critical Point should be better than other point.For High Dimensional Systems, always not there is above-mentioned character, but roughly rule still has.Certainly, the character of Jacobian matrix not determines the single factor of algorithm the convergence speed, and adopt Newton-Raphson approach to carry out the numerical solution of Nonlinear System of Equations, convergence of algorithm performance is also in close relations with initial value.

Continuous tide calculates general Newton-Raphson approach de-spread power flow equation.After Load flow calculation each time, if predict trend solution next time, and in this, as the initial value of Load flow calculation next time, obviously can greatly reduce the iterations of Load flow calculation, accelerate computational speed.

The essence of tangential method utilizes the differential of current solution to predict next trend solution.Can obtain the continuous tide fundamental equation of formula (1) differential of demanding perfection:

f _xdx+bdλ＝0(7)

If prediction direction is $y=\left(\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right),$ Then have

f _xΔx+bΔλ＝0(8)

If f _x ^tbe good state, make Δ λ=1, then

f _xΔx＝-b(9)

This equation of direct solution obtains Δ x, prediction direction $y=\left(\begin{array}{c}\mathrm{\Δ}x\\ 1\end{array}\right).$

For the initial point that continuous tide calculates, owing to only having current point information, Jacobian matrix is again good state, therefore general direct employing the method is predicted.

But Load Flow Jacobian Matrix is unusual in critical point place, Near The Critical Point morbid state, therefore critical point and near, the solving precision of formula (9) matrix equation cannot effectively be ensured, prediction effect may be poor.

To formula (8), make Δ x _k=-1,1≤k≤n, then have the formula of the trend solution predicting Load flow calculation next time:

$\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=\left[\begin{array}{c}0\\ -1\end{array}\right]---\left(10\right)$

Wherein, t _kbe a kth element be 1, all the other elements are the column vector of 0, namely

For hereafter illustrating conveniently, first provide following lemma.

Lemma 1: for matrix $M=\left[\begin{array}{cc}A& b\\ c& d\end{array}\right],$ When A is unusual, and time dimnull (A)=1, and if only if $b\∉Range\left(A\right),c^T\∉Range\left(A^T\right)$ Time, M is nonsingular.

If critical point is normal flex point, then critical point place dimnull (f _x)=1, and now suppose f _xscratch the residual matrix f ' after row k kth row _xbe good state, then have from lemma 1, matrix $\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]$ Nonsingular.

From upper joint, if select the element of k corresponding to a certain weak node voltage, then f ' _xto be good state, therefore only according to the weak node of the prediction direction of last time or sensitivity analysis certainty annuity, and subscript k, then direct solution formula (10) need be selected according to this, prediction direction y, Here it is tangent line predicted method.

At Near The Critical Point, if direct solution formula (10), owing to expanding the left sub matrix morbid state of Load Flow Jacobian Matrix, the computational accuracy of matrix equation cannot effectively be ensured, prediction effect may be poor.

By Δ x _kbe used as constant, namely scratch formula (10) last column and by f _xkth row move to right-hand vector, then the row k of equation is moved to last column, solve this equation prediction direction y.

Through above-mentioned process, forecasting process effectively overcomes Load Flow Jacobian Matrix at the critical point place unusual Ji λ – V curve prediction of failure that Non-smooth surface may cause before and after node type transforms, and substantially increases precision and the robustness of forecasting process.

After giving prediction direction, also need to provide step-length h, could future position be determined.Step-length selects there is important impact to the performance of Continuation Method.Step-length obtains too little, and Load flow calculation can Fast Convergent each time, but will calculate and just can calculate Near The Critical Point many times, and to calculate the lower branch of λ – V curve, then required number of times is more.Step-length obtains too large, and the distance of future position and required point may be comparatively far away, and the iterations each time needed for Load flow calculation is more, and the possibility of result spends more computing time on the contrary, continuous tide even may be caused to calculate and do not restrain.

Generally speaking, the basic principle that step-length is selected is that step-length gets higher value in curve more smooth part; The part relatively bent at curve then gets smaller value.Here get wherein h _maxbe a given constant, y _ifor i-th component of prediction direction y.Obviously, the method meets above-mentioned basic principle.Simulation calculation also demonstrates the validity of the method.

In addition, in continuous tide calculates, also can introduce the concept of variable step, if the iterations needed for the calculating of this continuous tide reduces step-length more at most, increase step-length more at least, moderate, keep former step-length.

The ability of generator maintenance set end voltage affects the voltage stability of electric power system to a great extent.In the electric power system of reality, generator is subject to the restriction of maximum exciting current and heating in winding condition, and it is idle exerts oneself is limited.Here suppose generator reactive exert oneself once reach its upper limit, by maximum for maintenance idle exert oneself constant.From the viewpoint of Load flow calculation, Here it is, and generator is PQ node from PV Node.Generator reactive restriction of exerting oneself is one of most important non-linear factor in static electric voltage stability research, whether considers the reasonability that generator reactive restriction directly will have influence on critical point and calculates.If do not consider that generator reactive is exerted oneself restriction, result of calculation will be partial to optimism.

State index method only calculates current state, therefore generally cannot consider the idle restriction of exerting oneself of generator.For Continuation Method, then must consider this factor.

Fig. 6 to Fig. 8 give a certain generator reactive exert oneself reach the upper limit after from PV Node be PQ node (Q=Q ^max) three kinds of situations of change that Shi λ – V Curves may occur.Wherein, curve I is λ – V curve when this generator being used as PV node processing, and curve II is λ – V curve when this generator being used as PQ node processing, and bold portion is then for considering the actual λ – V curve during restriction of this generator reactive.

As can be seen from Fig. 6 to Fig. 8, when generator is PQ node from PV Node, actual λ – V curve will be continuous and Non-smooth surface.

For the situation of Fig. 6, two λ – V curves meet at first respective branch, and its actual critical point is the critical point of this generator when being used as PQ node processing.For the situation of Fig. 7 and Fig. 8, first branch of curve I and second branch of curve II, in fact its intersection point is exactly voltage collapse critical point, therefore carries out should obtaining its intersection point when continuous tide calculates.Fig. 8 is in fact similar to Fig. 7, two kinds of different situations that just may occur due to the multi-solution of trend.

Predict according to linear prediction method, for Fig. 6 situation, because the graded of actual λ – V curve in breakover point both sides is not very large, the distance of future position and actual λ – V curve is not generally far, convergence still can be guaranteed, and just required iterations may be relatively many; For Fig. 7 situation, the graded of breakover point both sides is comparatively large, and future position may away from actual λ – V curve, and it is generally more that continuous tide calculates required iterations, even may not restrain; For the situation of Fig. 8, then may not restrain or even converge on false branches.

Above-mentioned analysis shows, when consideration generator reactive exerts oneself restriction, according to linear prediction method, then continuous tide calculates and is restricted idle exerting oneself, and should use tangent line predicted method instead and predict when machine end node generation node type transforms, this adds the complexity of algorithm undoubtedly, according to improvement tangent line predicted method, though the amount of calculation needed for it increases to some extent, need not transform between multiple Forecasting Methodology, prediction effect is also relatively better, therefore suggestion adopts improvement tangent line predicted method.Certainly, if do not consider, generator reactive is exerted oneself restriction, then can adopt linear prediction method.

Based on same inventive concept, additionally provide a kind of Voltage Stability Analysis device of wind energy turbine set electric power system in the embodiment of the present invention, as described in the following examples.The principle of dealing with problems due to the Voltage Stability Analysis device of wind energy turbine set electric power system is similar to the Voltage Stability Analysis method of wind energy turbine set electric power system, therefore the enforcement of the Voltage Stability Analysis device of wind energy turbine set electric power system see the enforcement of the Voltage Stability Analysis method of wind energy turbine set electric power system, can repeat part and repeats no more.Following used, term " unit " or " module " can realize the software of predetermined function and/or the combination of hardware.Although the device described by following examples preferably realizes with software, hardware, or the realization of the combination of software and hardware also may and conceived.

Fig. 9 is a kind of structured flowchart of the Voltage Stability Analysis device of the wind energy turbine set electric power system of the embodiment of the present invention, as shown in Figure 9, comprise: equation is expanded correcting module 901, solved module 902, determination module 903 and analysis module 904, is described below to this structure.

Equation expansion correcting module 901, new equation is formed for selecting serialization parameter, utilize the power flow equation of described new equation extended power system, the power flow equation of the electric power system after expansion is revised, obtain the power flow equation of revised electric power system, in the power flow equation of revised electric power system, revised Load Flow Jacobian Matrix is the Load Flow Jacobian Matrix of maximum node when being used as the node processing that injecting power and voltage magnitude all specify that declined by voltage magnitude in electric power system;

Solve module 902, expanding correcting module 901 with equation and be connected, for adopting the power flow equation of revised electric power system described in Newton-Raphson approach iterative, obtaining prediction direction;

Determination module 903, and solves module 902 and is connected, and for according to described prediction direction and the step-length preset, determines future position;

Analysis module 904, is connected with determination module 903, for analyzing the voltage stabilization situation of wind energy turbine set electric power system according to described future position.

In one embodiment, the power flow equation of described revised electric power system is:

$J^{\′\′}\left[\begin{array}{c}\mathrm{\Δ}{x}^{\′}\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=-\left[\begin{array}{c}{f}^{\′}\left(x\right)+{\mathrm{\λb}}^{\′}\\ f_k\left(x\right)+{\mathrm{\λb}}_k\end{array}\right]$

Wherein, x is state vector, and f (x) is trend equilibrium equation, and k is line number; $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ J " is the Jacobian matrix of the power flow equation of the electric power system of revised expansion; F ' _xit is revised Load Flow Jacobian Matrix; B ' is revised load growth direction b; b _kfor a kth element of b; X ' is revised vector x; F ' (x) is revised power flow equation group; f _kan x kth element that () is vector function f (x); f _{kx '}for function f _kx () is to the gradient vector of x '; Δ x ' is the change vector corresponding with x ', and Δ λ is the variable quantity of the horizontal λ of wind power output.

In one embodiment, module is solved, specifically for when after previous Load flow calculation, by the trend solution of following formula predictions Load flow calculation next time, and using the initial value of the trend solution of prediction as Load flow calculation next time described in:

$\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=\left[\begin{array}{c}0\\ -1\end{array}\right]$

Wherein, t _kbe a kth element be 1, all the other elements are the column vector of 0; B is load growth direction; f _xit is the Jacobian matrix of the power flow equation of electric power system; Δ λ is the variable quantity of the horizontal λ of wind power output; Δ x is state variation vector; Δ x _kthe row k element of Δ x, by Δ x _kbe used as constant.

In one embodiment, also comprise: step size computation module, the step-length for by presetting described in following formulae discovery:

$h=h_{max}/\underset{i=1}{\overset{n}{\max }}\left(y_i\right)$

Wherein, h is default step-length; h _maxfor constant; y _ifor i-th component of prediction direction y, n is positive integer.

In embodiments of the present invention, by the power flow equation utilizing new equation to carry out extended power system, the power flow equation after expanding is made to be the equation can trying to achieve definite value solution, and by revising the power flow equation of the electric power system after expansion, revised Load Flow Jacobian Matrix is made to be Load Flow Jacobian Matrix when weak node most in electric power system being used as PV node processing, namely the power flow equation of revised electric power system Jacobian matrix critical point and near be nonsingular, and amended Load Flow Jacobian Matrix (i.e. the Jacobian matrix left sub matrix of the power flow equation of revised electric power system) critical point and near be also nonsingular, solve the singular problem of expansion Load Flow Jacobian Matrix left sub matrix (i.e. Load Flow Jacobian Matrix) critical point place, overcome the harmful effect that the unusual and neighbouring morbid state of Load Flow Jacobian Matrix critical point place is brought to numerical computations, the computational accuracy of expansion update equation can effectively be ensured, continuous tide calculates and greatly improves in the convergence of Near The Critical Point, add the reliability of algorithm.

Obviously, those skilled in the art should be understood that, each module of the above-mentioned embodiment of the present invention or each step can realize with general calculation element, they can concentrate on single calculation element, or be distributed on network that multiple calculation element forms, alternatively, they can realize with the executable program code of calculation element, thus, they can be stored and be performed by calculation element in the storage device, and in some cases, step shown or described by can performing with the order be different from herein, or they are made into each integrated circuit modules respectively, or the multiple module in them or step are made into single integrated circuit module to realize.Like this, the embodiment of the present invention is not restricted to any specific hardware and software combination.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, for a person skilled in the art, the embodiment of the present invention can have various modifications and variations.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (8)

1. a Voltage Stability Analysis method for wind energy turbine set electric power system, is characterized in that, comprising:

Serialization parameter is selected to form new equation, utilize the power flow equation of described new equation extended power system, the power flow equation of the electric power system after expansion is revised, obtain the power flow equation of revised electric power system, in the power flow equation of revised electric power system, revised Load Flow Jacobian Matrix is the Load Flow Jacobian Matrix of maximum node when being used as the node processing that injecting power and voltage magnitude all specify that declined by voltage magnitude in electric power system;

Adopt the power flow equation of revised electric power system described in Newton-Raphson approach iterative, obtain prediction direction;

According to described prediction direction and default step-length, determine future position;

The voltage stabilization situation of wind energy turbine set electric power system is analyzed according to described future position.

2. the Voltage Stability Analysis method of wind energy turbine set electric power system as claimed in claim 1, it is characterized in that, the power flow equation of described revised electric power system is:

$J^{\′\′}\left[\begin{array}{c}{\mathrm{\Δx}}^{\′}\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=-\left[\begin{array}{c}{f}^{\′}\left(x\right)+{\mathrm{\λb}}^{\′}\\ f_k\left(x\right)+{\mathrm{\λb}}_k\end{array}\right]$

Wherein, x is state vector; F (x) is trend equilibrium equation, and k is line number; $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ J " is the Jacobian matrix of revised extended power flow equations; f _x' be revised Load Flow Jacobian Matrix; B ' is revised load growth direction; b _kfor a kth element of b; X ' is revised state vector; F ' (x) is revised power flow equation group; f _kan x kth element that () is vector function f (x); f _{kx '}for function f _kx () is to the gradient vector of x '; Δ x ' is the change vector corresponding with x ', and Δ λ is the variable quantity of the horizontal λ of wind power output.

3. the Voltage Stability Analysis method of wind energy turbine set electric power system as claimed in claim 1, is characterized in that, adopts the power flow equation of revised electric power system described in Newton-Raphson approach iterative, comprising:

When after previous Load flow calculation, by the trend solution of following formula predictions Load flow calculation next time, and using the initial value of the trend solution of prediction as Load flow calculation next time:

$\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=\left[\begin{array}{c}0\\ -1\end{array}\right]$

Wherein, t _kbe a kth element be 1, all the other elements are the column vector of 0; B is load growth direction; f _xit is the Jacobian matrix of the power flow equation of electric power system; Δ λ is the variable quantity of the horizontal λ of wind power output, and Δ x is state variation vector, Δ x _kthe row k element of Δ x, by Δ x _kbe used as constant.

4. the Voltage Stability Analysis method of wind energy turbine set electric power system as claimed any one in claims 1 to 3, is characterized in that, the step-length by presetting described in following formulae discovery:

$h=h_{max}/\underset{i=1}{\overset{n}{\max }}\left(y_i\right)$

Wherein, h is default step-length; h _maxfor constant; y _ifor i-th component of prediction direction y, n is positive integer.

5. a Voltage Stability Analysis device for wind energy turbine set electric power system, is characterized in that, comprising:

Equation expansion correcting module, new equation is formed for selecting serialization parameter, utilize the power flow equation of described new equation extended power system, the power flow equation of the electric power system after expansion is revised, obtain the power flow equation of revised electric power system, in the power flow equation of revised electric power system, revised Load Flow Jacobian Matrix is the Load Flow Jacobian Matrix of maximum node when being used as the node processing that injecting power and voltage magnitude all specify that declined by voltage magnitude in electric power system;

Solving module, for adopting the power flow equation of revised electric power system described in Newton-Raphson approach iterative, obtaining prediction direction;

Determination module, for according to described prediction direction and default step-length, determines future position;

Analysis module, for analyzing the voltage stabilization situation of wind energy turbine set electric power system according to described future position.

6. the Voltage Stability Analysis device of wind energy turbine set electric power system as claimed in claim 5, it is characterized in that, the power flow equation of described revised electric power system is:

$J^{\′\′}\left[\begin{array}{c}{\mathrm{\Δx}}^{\′}\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=-\left[\begin{array}{c}{f}^{\′}\left(x\right)+{\mathrm{\λb}}^{\′}\\ f_k\left(x\right)+{\mathrm{\λb}}_k\end{array}\right]$

Wherein, x is state vector, and f (x) is trend equilibrium equation, and k is line number; $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ J " is the Jacobian matrix of the power flow equation of the electric power system of revised expansion; f _x' be revised Load Flow Jacobian Matrix; B ' is revised load growth direction b; b _kfor a kth element of b; X ' is revised vector; F ' (x) is revised power flow equation group; f _kan x kth element that () is vector function f (x); f _{kx '}for function f _kx () is to the gradient vector of x '; Δ x ' is the change vector corresponding with x ', and Δ λ is the variable quantity of the horizontal λ of wind power output.

7. the Voltage Stability Analysis device of wind energy turbine set electric power system as claimed in claim 5, it is characterized in that, describedly solve module, specifically for when after previous Load flow calculation, by the trend solution of following formula predictions Load flow calculation next time, and using the initial value of the trend solution of prediction as Load flow calculation next time:

$\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=\left[\begin{array}{c}0\\ -1\end{array}\right]$

Wherein, t _kbe a kth element be 1, all the other elements are the column vector of 0; B is load growth direction; f _xit is the Jacobian matrix of the power flow equation of electric power system; Δ λ is the variable quantity of the horizontal λ of wind power output; Δ x is state variation vector; Δ x _kthe row k element of Δ x, by Δ x _kbe used as constant.

8. the Voltage Stability Analysis device of the wind energy turbine set electric power system according to any one of claim 5 to 7, is characterized in that, also comprise:

Step size computation module, the step-length for by presetting described in following formulae discovery:

$h=h_{max}/\underset{i=1}{\overset{n}{\max }}\left(y_i\right)$

Wherein, h is default step-length; h _maxfor constant; y _ifor i-th component of prediction direction y, n is positive integer.