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

Abstract

Embodiments of the present invention provide a voltage stability analysis method and device for a wind farm power system, wherein the method includes: selecting continuous parameters to form a new equation, using the new equation to expand the power flow equation of the power system, and expanding The revised power flow equation of the power system is corrected to obtain the revised power flow equation of the power system. In the revised power flow equation of the power system, the revised power flow Jacobian matrix is the node where the voltage amplitude drops the most in the power system The power flow Jacobian matrix when treated as a node with specified injected power and voltage amplitude; the Newton-Raphson method is used to iteratively solve the power flow equation of the revised power system to obtain the predicted direction; according to the predicted direction and predicted Determine the prediction point according to the set step size; analyze the voltage stability of the wind farm power system according to the prediction point. The convergence of continuous power flow calculation in this scheme is greatly improved near the critical point, which increases the reliability of the algorithm.

Description

Voltage stability analysis method and device for wind farm power system

technical field

The invention relates to the technical field of electric power safety, in particular to a voltage stability analysis method and device for a wind farm power system.

Background technique

The reactive power characteristics of the wind farm are related to the active power characteristics of the wind farm. When the active output of the wind farm is low, the transmission line is lightly loaded, and the reactive power of line charging is excessive, the wind turbine should absorb reactive power. If the reactive power absorbed by the wind turbine is insufficient, the wind farm will inject reactive power into the grid, and high voltage problems may occur. When the active power output of the wind farm increases, the transmission line is overloaded, and the inductive reactive power consumed increases accordingly. The reactive power charged by the line is not enough to offset the inductive reactive power consumed by the line and main transformer and other components. The wind turbine should generate reactive power . If the reactive power generated by the wind turbine is insufficient, the wind farm will absorb reactive power from the grid. If the wind farm absorbs reactive power from the grid, it may cause the voltage drop of the wind farm. Therefore, when the reactive power of the grid is insufficient and the active power output of the wind turbine is large or full, there may be voltage stability problems, and it is necessary to conduct a detailed voltage stability analysis.

The continuum power flow method is one of the basic methods of voltage stability analysis. By selecting certain continuation parameters to ensure the convergence of the power flow calculation at the critical point and its vicinity, and introducing mechanisms such as prediction, correction, and step size adjustment, it is possible to reduce the The number of iterations required for the calculation process reduces the amount of calculation. It iterates repeatedly at each point of the λ–V curve to calculate the accurate power flow, so it can obtain accurate information such as the λ–V curve, and can consider certain nonlinear control and inequality constraints, and has strong robustness sex.

The existing continuous flow method generally adds an equation to the basic equation of the continuous flow, and at the same time takes λ as a variable, so that a row and a column are added to the lower right of the Jacobian matrix. Even if the extended Jacobian matrix is at the critical point However, the part in the upper left corner is still singular at the critical point, so the convergence of the continuous power flow calculation near the critical point is difficult to be effectively guaranteed, and the reliability of the algorithm is greatly affected, which in turn affects the Reliability for voltage stability analysis of wind farm power systems.

Contents of the invention

The embodiment of the present invention provides a voltage stability analysis method of a wind farm power system to solve the technical problems in the prior art that the convergence of the continuous power flow calculation near the critical point is difficult to be effectively guaranteed and the reliability of the algorithm is greatly affected . The method includes: selecting continuous parameters to form a new equation, using the new equation to expand the power flow equation of the power system, and correcting the expanded power flow equation to obtain the revised power system. In the power flow equation of the final power system, the modified power flow Jacobian matrix is the power flow Jacobian matrix when the node in the power system with the largest drop in voltage amplitude is treated as a node with specified injected power and voltage amplitude; Newton - Raphson's method iteratively solves the power flow equation of the revised power system to obtain the predicted direction; according to the predicted direction and the preset step size, determine the predicted point; analyze the voltage stability of the wind farm power system according to the predicted point Condition.

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

${\mathrm{<span\; class="notranslate">\; J</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right]$

Among them, x is the state vector; f(x) is the power flow balance equation, and k is the row number; $J^{\&prime;\&prime;}=\left[\begin{array}{cc}{f}_x^{\&prime;}& b^{\&prime;}\\ f_{x^{\&prime;}}^T& b_k\end{array}\right],$ J″ is the modified Jacobian matrix of the extended power flow equation; f′ _x is the modified Jacobian matrix of the power flow; b′ is the direction of load growth after modification; b _k is the kth element of b; x′ is the modified f'(x) is the revised power flow equation system; f _k (x) is the kth element of the vector function f(x); f _kx' is the function f _k (x) to x' Gradient vector; Δx' is the change vector corresponding to x', and Δλ is the change amount of wind power output level λ.

In one embodiment, the Newton-Raphson method is used to iteratively solve the power flow equation of the revised power system, including: after the current power flow is calculated, the following formula is used to predict the power flow solution of the next power flow calculation, and the predicted power flow The solution is used as the initial value for the next power flow calculation:

$\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}& \mathrm{<span\; class="notranslate">\; b</span>}\\ {{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

Among them, t _k is a column vector whose kth element is 1 and the rest are 0; b is the direction of load growth; f _x is the Jacobian matrix of the power flow equation of the power system; Δλ is the variation of wind power output level λ, Δx is the state change vector, Δx _k is the kth row element of Δx, and Δx _k is regarded as a constant.

In one embodiment, the preset step size is calculated by the following formula:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; /</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$

Wherein, h is a preset step size; h _max is a constant; y _i is the i-th component of the prediction direction y, and n is a positive integer.

The embodiment of the present invention also provides a voltage stability analysis device for a wind farm power system to solve the problem in the prior art that the convergence of the continuous power flow calculation near the critical point is difficult to be effectively guaranteed and the reliability of the algorithm is greatly affected question. The device includes: an equation expansion correction module, which is used to select continuous parameters to form a new equation, use the new equation to expand the power flow equation of the power system, and correct the power flow equation of the expanded power system to obtain the corrected power The power flow equation of the system, in the revised power flow equation of the power system, the revised power flow Jacobian matrix is when the node in the power system with the largest drop in voltage amplitude is treated as a node with specified injected power and voltage amplitude The power flow Jacobian matrix; the solution module is used to iteratively solve the power flow equation of the revised power system by the Newton-Raphson method to obtain the predicted direction; the determination module is used to determine the direction according to the predicted direction and the preset step size, Determine the prediction point; the analysis module is used to analyze the voltage stability of the wind farm power system according to the prediction point.

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

${\mathrm{<span\; class="notranslate">\; J</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right]$

Among them, x is the state vector, f(x) is the power flow balance equation, and k is the row number; $J^{\&prime;\&prime;}=\left[\begin{array}{cc}{f}_x^{\&prime;}& b^{\&prime;}\\ f_{x^{\&prime;}}^T& b_k\end{array}\right],$ J″ is the modified Jacobian matrix of the power flow equation of the extended power system; f′ _x is the modified Jacobian matrix of the power flow; b′ is the modified load growth direction b; b _k is the kth element of b ; x' is the corrected vector; f'(x) is the revised power flow equation; f _k (x) is the kth element of the vector function f(x); f _kx' is the function f _k (x) Gradient vector to x';Δx' is the change vector corresponding to x', and Δλ is the change amount of wind power output level λ.

In one embodiment, the solution module is specifically used to predict the power flow solution for the next power flow calculation through the following formula after the current power flow calculation, and use the predicted power flow solution as the initial value for the next power flow calculation:

$\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}& \mathrm{<span\; class="notranslate">\; b</span>}\\ {{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

Among them, t _k is a column vector whose kth element is 1 and the rest are 0; b is the direction of load growth; f _x is the Jacobian matrix of the power flow equation of the power system; Δλ is the variation of wind power output level λ; Δx is the state change vector; Δx _k is the k-th row element of Δx, and Δx _k is regarded as a constant.

In one embodiment, it also includes: a step size calculation module, which is used to calculate the preset step size by the following formula:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; /</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$

Wherein, h is a preset step size; h _max is a constant; y _i is the i-th component of the prediction direction y, and n is a positive integer.

In the embodiment of the present invention, the power flow equation of the power system is extended by using a new equation, so that the extended power flow equation is an equation that can obtain a fixed value solution, and by correcting the extended power flow equation of the power system, The modified power flow Jacobian matrix is the power flow Jacobian matrix when the weakest node in the power system (that is, the node with the largest drop in voltage amplitude) is treated as a PV node (that is, a node with specified injected power and voltage amplitude) , that is, the Jacobian matrix of the modified power system power flow equation is non-singular at and near the critical point, and the modified power flow Jacobian matrix (that is, the Jacobian matrix in the upper left corner of the modified power system power flow equation ) is also non-singular at the critical point and its vicinity, which solves the singularity problem at the critical point of the matrix in the upper left corner of the extended power flow Jacobian matrix (ie, the power flow Jacobian matrix), and overcomes the singularity at the critical point of the power flow Jacobian matrix and its vicinity Due to the adverse effects of ill-conditioning on numerical calculation, the calculation accuracy of the extended correction equation can be effectively guaranteed, and the convergence of continuous power flow calculation near the critical point is greatly improved, which increases the reliability of the algorithm.

Description of drawings

The drawings described here are used to provide further understanding of the present invention, constitute a part of the application, and do not limit the present invention. In the attached picture:

Fig. 1 is a flow chart of a voltage stability analysis method for a wind farm power system provided by an embodiment of the present invention;

Fig. 2 is a schematic illustration of a point-by-point calculation method provided by an embodiment of the present invention;

Fig. 3 is an explanatory schematic diagram of a continuous arc length method provided by an embodiment of the present invention;

Fig. 4 is a schematic illustration of a homotopy continuation method provided by an embodiment of the present invention;

Fig. 5 is a schematic illustration of a local parameter continuation method provided by an embodiment of the present invention;

Fig. 6 is one of the schematic diagrams of the λ-V curve when considering reactive power limitation provided by the embodiment of the present invention;

Fig. 7 is the second schematic diagram of a λ-V curve when considering reactive power limitation provided by the embodiment of the present invention;

Fig. 8 is the third schematic diagram of a λ-V curve when considering reactive power limitation provided by the embodiment of the present invention;

Fig. 9 is a structural block diagram of a voltage stability analysis device for a wind farm power system provided by an embodiment of the present invention.

detailed description

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be described in further detail below in conjunction with the embodiments and accompanying drawings. Here, the exemplary embodiments and descriptions of the present invention are used to explain the present invention, but not to limit the present invention.

In an embodiment of the present invention, a voltage stability analysis method of a wind farm power system is provided, as shown in FIG. 1 , the method includes:

Step 101: Select continuous parameters to form a new equation, use the new equation to expand the power flow equation of the power system, and correct the expanded power flow equation to obtain the revised power system power flow equation. After the correction In the power flow equation of the power system, the modified power flow Jacobian matrix is the power flow Jacobian matrix when the node in the power system with the largest drop in voltage amplitude is treated as a node with specified injected power and voltage amplitude;

Step 102: Using the Newton-Raphson method to iteratively solve the power flow equation of the revised power system to obtain the predicted direction;

Step 103: Determine the prediction point according to the prediction direction and the preset step size;

Step 104: Analyze the voltage stability of the wind farm power system according to the prediction points.

It can be seen from the process shown in Figure 1 that in the embodiment of the present invention, the power flow equation of the power system is expanded by using a new equation, so that the expanded power flow equation is an equation that can obtain a fixed value solution, and the extended The power flow equation of the power system is corrected, so that the revised Jacobian matrix of the power system takes the weakest node in the power system (that is, the node with the largest voltage amplitude drop) as the PV node (that is, the injection power and voltage amplitude are both specified Node) when processing the power flow Jacobian matrix, that is, the Jacobian matrix of the revised power system power flow equation is non-singular at and near the critical point, and the modified power flow Jacobian matrix (that is, the revised power system power flow The upper left part of the Jacobian matrix of the equation) is also non-singular at the critical point and its vicinity, which solves the singularity problem at the critical point of the extended current Jacobian matrix (that is, the upper left part of the current Jacobian matrix) and overcomes the Comparable to the adverse effects of the singularity at the critical point of the matrix and its ill-conditioning near the numerical calculation, the calculation accuracy of the extended correction equation can be effectively guaranteed, and the convergence of the continuous power flow calculation near the critical point is greatly improved, which increases the reliability of the algorithm.

In the specific implementation, since the power flow equation of the power system extended by the above new equation is an equation that can obtain a fixed value solution, and the extended Jacobian matrix is non-singular at the critical point, but the extended Jacobian matrix Part of the matrix in the upper left corner (that is, the conventional power flow Jacobian matrix) is singular at the critical point and ill-conditioned near the critical point, making it difficult to effectively guarantee the calculation accuracy of the extended power flow equation at and near the critical point. The convergence of will also not be effectively guaranteed. Therefore, in order to realize that the upper left part of the extended Jacobian matrix (that is, the conventional power flow Jacobian matrix) is non-singular at the critical point, in this embodiment, the extended Jacobian The power flow equation of the power system is corrected, and the revised power flow equation of the power system is:

${\mathrm{<span\; class="notranslate">\; J</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right]$

Among them, x is the state vector, that is, the vector composed of the voltage amplitude and phase of each node; f(x) is the power flow balance equation, and k is the line number; $J^{\&prime;\&prime;}=\left[\begin{array}{cc}{f}_x^{\&prime;}& b^{\&prime;}\\ f_{x^{\&prime;}}^T& b_k\end{array}\right],$ J″ is the modified Jacobian matrix of the power flow equation of the extended power system; f′ _x is the revised Jacobian matrix of the power flow, that is, the remaining matrix after the k-th row and k-th column of the power flow Jacobian matrix are removed; b ' is the corrected load growth direction b, that is, the remaining vector after the k-th row is crossed out by b; b _k is the k-th element of b; Residual vector; f'(x) is the modified power flow equation system, that is, the remaining vector after the k-th line is removed from the function vector f(x); f _k (x) is the k-th element of the vector function f(x) ; f _kx' is the gradient vector of function f _k (x) to x';Δx' is the change vector corresponding to x', and Δλ is the variation of wind power output level λ. Specifically, take x _k as a constant, and Move the equation f _k (x)+λb _k =0 to the last row, it can be seen that J″ is actually J′ (i.e. the Jacobian matrix of the power flow equation after expansion) and the n+1th row is crossed out It is obtained by moving the k-th row to the last row after the k-th column, f′ _x is the matrix obtained by removing the k-th row and the k-th column of the conventional power flow Jacobian matrix f _x ; b’ is the vector b and removing the k-th element b _k is the kth element of the vector b; x' is the vector after the kth element of the vector x is crossed out; f'(x) is the vector function f(x) after the kth element is crossed out vector; f _k (x) is the kth element of the vector function f(x); f _kx′ is the gradient vector of the function f _k (x) to x′.

In specific implementation, the continuous power flow calculation adopts the Newton-Raphson method to solve the extended power flow equation. After each power flow calculation, if the next power flow solution is predicted and the predicted power flow solution is used as the initial value of the next power flow calculation, it is obvious that the number of iterations of the power flow calculation can be greatly reduced and the calculation speed can be accelerated. In order to improve the prediction success rate, improve the accuracy and robustness of the prediction process, in this embodiment, the Newton-Raphson method is used to iteratively solve the power flow equation of the revised power system, including: after the current power flow is calculated, by The following formula predicts the power flow solution of the next power flow calculation, and uses the predicted power flow solution as the initial value of the next power flow calculation:

$\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}& \mathrm{<span\; class="notranslate">\; b</span>}\\ {{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

Among them, t _k is a column vector whose kth element is 1 and the rest are 0; b is the direction of load growth; f _x is the Jacobian matrix of the power flow equation of the power system; Δλ is the variation of wind power output level λ, Δx is the state change vector, Δx _k is the k-th row element of Δx, take Δx _k as a constant, and Δx _k as a constant, that is, cross out the formula $\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;}x\\ \mathrm{\&Delta;}\mathrm{\&lambda;}\end{array}\right]=\left[\begin{array}{c}0\\ -1\end{array}\right]$ and move the k-th column of f _x to the right-hand term, and then move the k-th row of the equation to the last row, and solve the equation to get the predicted direction y.

In specific implementation, after the prediction direction is given, the step size h needs to be given to determine the prediction point. The choice of step size has a significant impact on the performance of the continuum power flow method. If the step size is too small, each power flow calculation can converge quickly, but it takes many calculations to reach the critical point. If the lower half branch of the λ–V curve is to be calculated, more times are required. If the step size is too large, the distance between the predicted point and the desired point may be far away, and the number of iterations required for each power flow calculation may be more. As a result, more calculation time may be spent instead, and the continuous power flow calculation may even not converge. Generally speaking, the basic principle of step size selection is to take a larger value for the step size in the flat part of the curve; take a smaller value for the curved part of the curve. Therefore, in this embodiment, the preset step size is calculated by the following formula:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; /</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$

Wherein, h is a preset step size; h _max is a constant; y _i is the i-th component of the prediction direction y, and n is a positive integer. Specifically, the concept of variable step size can also be introduced in the continuous power flow calculation. If the number of iterations required for this continuous power flow calculation is large, the step size will be reduced; if the number of iterations is small, the step size will be increased; Keep the original step size.

The voltage stability analysis method of the above-mentioned wind farm power system is described below in conjunction with specific examples. For example:

The basic power flow equation of the power system is:

f(x)+λb=0(1)

Among them, x∈R ⁿ ; f(x) is an n-dimensional function vector; b is the direction of load growth, b∈R ⁿ ; λ is an actual parameter variable, which actually represents the system to a certain extent load level.

The basic power flow equation of formula (1) has n+1 variables, but there are only n equations, and the fixed value solution cannot be solved. It is actually a curve on the n+1-dimensional space. In order to obtain a fixed value solution, it is necessary to add an equation. The simplest and most intuitive method is of course to use the point-by-point calculation method shown in Figure 2. In each power flow calculation, the value of λ is determined first, and then the corresponding fixed value solution can be obtained. However, when λ takes a certain large value, the correction equation may appear ill-conditioned, and as the value of λ continues to increase, its ill-conditioning will become more serious. The power flow calculation fails to converge. The illustration diagram of the point-by-point calculation method in Figure 2 illustrates this point intuitively. As the load level increases, the value of λ continues to increase, and the prediction point x _p moves to the right. When x _p x is tangent to the λ–V curve, x is the critical point of voltage collapse, but because the Jacobian matrix is at the critical point Singular, ill-conditioned near the critical point, the power flow calculation will not be able to converge, and the numerical calculation will fail. In order to overcome this shortcoming, the continuum power flow method came into being.

The key of the continuum power flow method is to choose reasonable continuation parameters to ensure the convergence at and near the critical point. At present, the parameter continuation methods mainly include arc length continuation method, homotopy continuation method and local parameter continuation method.

Figure 3 intuitively shows the basic concept of the arc length continuation method. The basic idea is to introduce the parameter S to represent the arc length from x to the initial point x ₀ , and take S to be equal to the length of x ₀ x _p , that is, the new The increasing equation is:

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

in, $S^2-\underset{i=1}{\overset{\mathrm{no}}{\&Sigma;}}{(x_{ip}-x_{i0})}^2+{({\mathrm{\&lambda;}}_p-{\mathrm{\&lambda;}}_0)}^2.$

Figure 4 intuitively shows the basic concept of the homotopy continuation method. The basic idea is to make the vector xx _p perpendicular to the vector x ₀ -x _p , so that the equation (namely the above new equation) can be added:

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Figure 5 visually illustrates the basic concept of the local parameter continuation method. The basic idea is to first determine a certain element of the vector x according to the prediction direction, that is, to increase the equation (namely the above new equation) according to x ₀ and x _p :

x _k = x _pk (4)

Among them, k is the subscript corresponding to the local continuation parameter. In practice, the subscript corresponding to the element with the largest absolute value of the vector x _p -x ₀ is generally taken. For continuous power flow calculation, k can be limited to the element corresponding to the voltage.

After the above processing, the expanded power flow equation has n+1 equations and n+1 variables, from which the fixed value solution can be obtained.

For the convenience of description, the above added equations (ie, the above new equations) are collectively represented by g(x,λ)=0. Using the Newton-Raphson method to solve the extended power flow equation, the corresponding extended power flow equation is as follows:

${\mathrm{<span\; class="notranslate">\; J</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\mathrm{<span\; class="notranslate">\; b</span>}\\ \mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

in, $J^{\&prime;}=\left[\begin{array}{cc}{f}_x& b\\ t_x^T& g_{\mathrm{\&lambda;}}\end{array}\right],$ J=f _x is the Jacobian matrix of the conventional power flow, J′ is the Jacobian matrix of the expanded power flow equation, and the superscript T represents transposition.

If the critical point is a normal inflection point (ie saddle node bifurcation point), the Jacobian matrix J' of the extended power flow equation is non-singular at the critical point.

For the solution of the extended equation (5), since the extended power flow Jacobian matrix J′ is non-singular at the critical point, if the triangular decomposition selects the pivot, the method can reliably calculate the voltage collapse critical point. However, due to the consideration of sparsity, the pivot is generally not selected for the triangular decomposition of the Jacobian matrix, and because the matrix f _x in the upper left corner of J′ (that is, the conventional power flow Jacobian matrix) is singular at the critical point and ill-conditioned near the critical point, This makes it difficult to effectively guarantee the calculation accuracy of the extended equation at and near the critical point, and the convergence of the continuum power flow method at and near the critical point cannot be effectively guaranteed either.

In order to overcome the above shortcomings, the algorithm implementation of the local parameter continuation method is modified appropriately. In the process of iteratively solving the intersection of the λ–V curve and the newly added equation x _k = x _pk , x _k = x _pk is not considered as an equation, but x _k is regarded as a constant, and the equation f _k ( x)+λb _k =0 moves to the last row. Correspondingly, the Newton-Raphson method is used to iteratively solve the corresponding correction equation (that is, the power flow equation of the above-mentioned revised power system) as follows:

${\mathrm{<span\; class="notranslate">\; J</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

in, $J^{\&prime;\&prime;}=\left[\begin{array}{cc}{f}_x^{\&prime;}& b^{\&prime;}\\ f_{x^{\&prime;}}^T& b_k\end{array}\right],$ J″ is the above-mentioned modified Jacobian matrix of the current flow; f′ _x is the matrix after the k-th row and the k-column of f _x are crossed out; b’ is the vector after the k-th element of the vector b is crossed out; b _k is the vector b The k-th element of ; x' is the vector after the k-th element of the vector x is crossed out; f'(x) is the vector after the k-th element of the vector function f(x) is crossed out; f _k (x) is the vector The kth element of the function f(x); f _kx' is the gradient vector of the function f _k (x) to x'.

It can be seen that J″ is actually obtained by crossing out the n+1th row and kth column of J′ and moving the kth row to the last row.

For the local parameter continuous method, in formula (5) Now suppose that J″ is singular at the critical point, then Make J″w=0. Construct vector w′=(w ₁ ,w ₂ ,...,w _k-1 ,0,w _k ,...,w _n ) ^T , then J′w′=0 From w≠0, w′≠0 can be obtained, so J′ is singular. This contradicts that J′ is non-singular at the normal inflection point, which proves that if the critical point is a normal inflection point, J″ is non-singular at the critical point.

For power system continuous power flow calculation, at the critical point of voltage collapse and its vicinity, according to the selection principle of the subscript k above, x _k should correspond to the voltage of the node with the fastest voltage drop, which shows that f′ _x is the weakest node of the system as The power flow Jacobian matrix when PV nodes are processed. From a physical point of view, treating a node as a PV node actually means that the node voltage remains constant. It is conceivable that if a sufficient reactive power supply is put into a weak node of the system to maintain a constant voltage of the node, the voltage stability margin of the system will increase, which means that the critical point of f′ _x is non-singular. It can be seen that even at the critical point, f′ _x and J″ are not singular, and the continuum power flow method can reliably calculate the critical point of voltage collapse.

From the perspective of spatial analytic geometry, each point in the continuous power flow calculation is equivalent to finding the intersection point between the λ–V curve and the space surface corresponding to the newly added equation. Use the Newton-Raphson method to iteratively solve the intersection point of a curve and a surface in a multi-dimensional space. When the curve is tangent to the surface, the corresponding Jacobian matrix is singular, and the numerical calculation will not converge. When it is orthogonal, its convergence should be the best. Well, its convergence at intersection is somewhere in between. The positive singularity at the critical point of the Jacobian matrix of the power flow equation comes from the tangency between the λ–V curve and the λ constant surface. For the continuum power flow method, since the space surface corresponding to the new equation is no longer tangent to the λ–V curve but intersects, the extended Jacobian matrix of the power flow is no longer singular.

Since the previous continuum power flow method did not solve the ill-conditioning of the upper left corner of the extended power flow Jacobian matrix caused by the ill-conditioning of the conventional power flow Jacobian matrix near the critical point, the calculation accuracy of the extended correction equation near the critical point is affected. The convergence of continuous power flow calculation cannot be effectively guaranteed. With this method, since the singularity at the critical point in the upper left corner of the extended power flow Jacobian matrix is resolved, the calculation accuracy of the extended correction equation can be effectively guaranteed, and the convergence of the continuous power flow calculation near the critical point is greatly improved. In fact, for a two-dimensional system, the space surface corresponding to the newly added equation of the local parameter continuation method is orthogonal to the λ–V curve at the critical point, and after the improvement of this project, the calculation accuracy of the extended correction equation can be effectively guaranteed , the convergence near the critical point should be better than other points. For high-dimensional systems, the above properties do not always exist, but there are general rules. Of course, the nature of the Jacobian matrix is not the only factor that determines the convergence speed of the algorithm. When the Newton-Raphson method is used to solve the nonlinear equations numerically, the convergence performance of the algorithm is also closely related to the initial value.

The continuous power flow calculation generally uses the Newton-Raphson method to solve the extended power flow equation. After each power flow calculation, if the next power flow solution is predicted and used as the initial value of the next power flow calculation, it is obvious that the number of iterations of the power flow calculation can be greatly reduced and the calculation speed can be accelerated.

The essence of the tangent method is to use the differential of the current solution to predict the next power flow solution. The total differential of the continuous power flow basic equation of formula (1) can be obtained:

f _x dx+bdλ=0(7)

Let the prediction direction be $\mathrm{the\; y}=\left(\begin{array}{c}\mathrm{\&Delta;}x\\ \mathrm{\&Delta;}\mathrm{\&lambda;}\end{array}\right),$ then there is

f _x Δx+bΔλ=0(8)

If f _x ^T is well-conditioned, let Δλ=1, then

f _x Δx = -b(9)

Solve this equation directly to get Δx, then you can get the predicted direction $\mathrm{the\; y}=\left(\begin{array}{c}\mathrm{\&Delta;}x\\ 1\end{array}\right).$

For the initial point of continuous power flow calculation, since there is only current point information and the Jacobian matrix is well-conditioned, this method is generally used directly for prediction.

However, the power flow Jacobian matrix is singular at the critical point and ill-conditioned near the critical point. Therefore, at the critical point and its vicinity, the solution accuracy of the matrix equation (9) cannot be effectively guaranteed, and the prediction effect may be poor.

For formula (8), if Δx _k = -1, 1≤k≤n, then there is a formula for predicting the power flow solution for the next power flow calculation:

$\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}& \mathrm{<span\; class="notranslate">\; b</span>}\\ {{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Among them, t _k is a column vector whose kth element is 1 and the rest of the elements are 0, namely

For the convenience of the following explanation, the following lemma is given first.

Lemma 1: For matrices $m=\left[\begin{array}{cc}A& b\\ c& d\end{array}\right],$ When A is singular, and dimnull(A)=1, if and only if $b\&NotElement;Ra\mathrm{no}ge\left(A\right),c^T\&NotElement;Ra\mathrm{no}ge\left(A^T\right)$ , M is non-singular.

If the critical point is a normal inflection point, dimnull(f _x )=1 at the critical point, and Assume now that the remaining matrix f′ _x after the k-th row and k-column of f _x is well-conditioned, then we have From Lemma 1, we know that the matrix $\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]$ non-singular.

It can be known from the previous section that if k is selected as the element corresponding to a weak node voltage, then f′ _x will be in a good state, so it is only necessary to determine the weak node of the system according to the last predicted direction or sensitivity analysis, and based on this Select the subscript k, and then directly solve the formula (10) to get the prediction direction y, which is the tangent prediction method.

Near the critical point, if the equation (10) is directly solved, the calculation accuracy of the matrix equation cannot be effectively guaranteed due to the ill-conditioned matrix of the upper left corner of the extended power flow Jacobian matrix, and the prediction effect may be poor.

Take Δx _k as a constant, that is, cross out the last line of formula (10) and move the kth column of f _x to the right-hand term, and then move the kth line of the equation to the last line, and solve the equation to get the predicted direction y.

After the above treatment, the prediction process effectively overcomes the possible prediction failure caused by the singularity of the power flow Jacobian matrix at the critical point and the non-smoothness of the λ–V curve before and after the node type transformation, greatly improving the accuracy and robustness of the prediction process.

After the prediction direction is given, the step size h needs to be given to determine the prediction point. The choice of step size has a significant impact on the performance of the continuum power flow method. If the step size is too small, each power flow calculation can converge quickly, but it takes many calculations to reach the critical point. If the lower half branch of the λ–V curve is to be calculated, more times are required. If the step size is too large, the distance between the predicted point and the desired point may be far away, and the number of iterations required for each power flow calculation may be larger. As a result, more calculation time may be spent instead, and the continuous power flow calculation may even cause non-convergence.

Generally speaking, the basic principle of step size selection is to take a larger value for the step size in the relatively flat part of the curve; take a smaller value for the curved part of the curve. Take here Among them, h _max is a given constant, and y _i is the i-th component of the prediction direction y. Obviously, this method satisfies the basic principles mentioned above. The simulation calculation also proves the validity of the method.

In addition, the concept of variable step size can also be introduced in the continuous power flow calculation. If the number of iterations required for this continuous power flow calculation is large, the step size will be reduced, if it is less, the step size will be increased, and if it is moderate, the original step size will be maintained.

The ability of the generator to maintain the terminal voltage greatly affects the voltage stability of the power system. In the actual power system, the generator is limited by the maximum excitation current and winding heating conditions, and its reactive power output is limited. It is assumed here that once the reactive power output of the generator reaches its upper limit, the maximum reactive power output will remain unchanged. From the point of view of power flow calculation, this is the conversion of generators from PV nodes to PQ nodes. Generator reactive power limitation is one of the most important nonlinear factors in the study of static voltage stability. Whether to consider generator reactive power limitation will directly affect the rationality of critical point calculation. If the limitation of reactive power output of the generator is not considered, the calculation result will be optimistic.

The state index method only calculates the current state, so it is generally unable to consider the reactive output limit of the generator. For the continuous flow method, this factor must be considered.

Figures 6 to 8 show three possible changes in the λ-V curve when a generator's reactive output reaches the upper limit and transforms from a PV node to a PQ node (Q=Q ^max ). Among them, curve I is the λ–V curve when the generator is treated as a PV node, curve II is the λ–V curve when the generator is treated as a PQ node, and the solid line is the Actual λ–V curves at work limitation.

It can be seen from Fig. 6 to Fig. 8 that when the generator is converted from PV node to PQ node, the actual λ-V curve will be continuous rather than smooth.

For the situation in Figure 6, the two λ-V curves intersect at their upper half branches, and the actual critical point is the critical point when the generator is treated as a PQ node. For the situation in Figure 7 and Figure 8, the intersection point of the upper half branch of curve I and the lower half branch of curve II is actually the critical point of voltage collapse, so the intersection point should be obtained when performing continuous power flow calculation. Figure 8 is actually similar to Figure 7, except for two different situations that may arise due to the multiple solutions of the power flow.

If the linear prediction method is used for prediction, for the situation in Figure 6, since the gradient change of the actual λ–V curve on both sides of the turning point is not very large, the distance between the prediction point and the actual λ–V curve is generally not very far, and the convergence of the algorithm is still It can be guaranteed, but the number of iterations required may be relatively large; for the situation in Figure 7, the gradient on both sides of the turning point changes greatly, and the predicted point may be far away from the actual λ–V curve, and the number of iterations required for continuous power flow calculation is generally more. It may not even converge; for the case of Fig. 8, it may not converge or even converge on the wrong branch.

The above analysis shows that when considering the limitation of reactive power output of generators, if the linear prediction method is adopted, the reactive power output of the continuous power flow calculation is limited, and the tangent prediction method should be used for prediction when the node type conversion occurs at the machine end node. The complexity of the algorithm is increased. If the improved tangent prediction method is used, the amount of calculation required will increase, but there is no need to convert between multiple prediction methods, and the prediction effect is relatively good. Therefore, it is recommended to use the improved tangent prediction method. Law. Of course, if the generator reactive power limit is not considered, the linear prediction method can be used.

Based on the same inventive concept, an embodiment of the present invention also provides a voltage stability analysis device for a wind farm power system, as described in the following embodiments. Since the problem-solving principle of the voltage stability analysis device of the wind farm power system is similar to the voltage stability analysis method of the wind farm power system, the implementation of the voltage stability analysis device of the wind farm power system can be found in the voltage stability analysis method of the wind farm power system implementation, the repetition will not be repeated. As used below, the term "unit" or "module" may be a combination of software and/or hardware that realizes a predetermined function. Although the devices described in the following embodiments are preferably implemented in software, implementations in hardware, or a combination of software and hardware are also possible and contemplated.

Fig. 9 is a structural block diagram of a voltage stability analysis device for a wind farm power system according to an embodiment of the present invention. As shown in Fig. 9, it includes: an equation extension correction module 901, a solution module 902, a determination module 903 and an analysis module 904, as follows This structure will be described.

The equation extension correction module 901 is used to select continuous parameters to form a new equation, use the new equation to expand the power flow equation of the power system, and correct the extended power flow equation of the power system to obtain the corrected power system flow equation In the revised power flow equation of the power system, the revised power flow Jacobian matrix is the power flow Jacobian when the node in the power system with the largest drop in voltage amplitude is treated as a node with specified injected power and voltage amplitude matrix;

The solution module 902 is connected to the equation extension correction module 901, and is used to iteratively solve the power flow equation of the corrected power system by using the Newton-Raphson method to obtain the predicted direction;

The determination module 903 is connected with the solution module 902, and is used to determine the prediction point according to the prediction direction and the preset step size;

The analysis module 904 is connected with the determination module 903, and is configured to analyze the voltage stability of the wind farm power system according to the prediction points.

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

${\mathrm{<span\; class="notranslate">\; J</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right]$

Among them, x is the state vector, f(x) is the power flow balance equation, and k is the row number; $J^{\&prime;\&prime;}=\left[\begin{array}{cc}{f}_x^{\&prime;}& b^{\&prime;}\\ f_{x^{\&prime;}}^T& b_k\end{array}\right],$ J″ is the modified Jacobian matrix of the power flow equation of the extended power system; f′ _x is the modified Jacobian matrix of the power flow; b′ is the modified load growth direction b; b _k is the kth element of b ; x′ is the modified vector x; f′(x) is the modified power flow equation; f _k (x) is the kth element of the vector function f(x); f _kx′ is the function f _k (x ) to the gradient vector of x';Δx' is the change vector corresponding to x', and Δλ is the variation of wind power output level λ.

In one embodiment, the solving module is specifically used to predict the power flow solution of the next power flow calculation through the following formula after the current power flow calculation, and use the predicted power flow solution as the initial value of the next power flow calculation:

$\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}& \mathrm{<span\; class="notranslate">\; b</span>}\\ {{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

Among them, t _k is a column vector whose kth element is 1 and the rest are 0; b is the direction of load growth; f _x is the Jacobian matrix of the power flow equation of the power system; Δλ is the variation of wind power output level λ; Δx is the state change vector; Δx _k is the k-th row element of Δx, and Δx _k is regarded as a constant.

In one embodiment, it also includes: a step calculation module, configured to calculate the preset step by the following formula:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; /</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$

Wherein, h is a preset step size; h _max is a constant; y _i is the i-th component of the prediction direction y, and n is a positive integer.

In the embodiment of the present invention, the power flow equation of the power system is extended by using a new equation, so that the extended power flow equation is an equation that can obtain a fixed value solution, and by correcting the extended power flow equation of the power system, The modified Jacobian matrix of the power flow is the Jacobian matrix of the power flow when the weakest node in the power system is treated as a PV node, that is, the Jacobian matrix of the power flow equation of the revised power system is non-singular at and near the critical point , and the modified power flow Jacobian matrix (that is, the Jacobian matrix in the upper left corner of the power flow equation of the revised power system) is also non-singular at and near the critical point, which solves the problem of extending the power flow Jacobian matrix in the upper left corner (i.e., the singularity problem at the critical point of the Jacobian matrix) overcomes the adverse effects on the numerical calculation caused by the singularity at the critical point of the Jacobian matrix and its nearby ill state, and the calculation accuracy of the extended correction equation can be effectively guaranteed. Continuous power flow The convergence of the calculation near the critical point is greatly improved, which increases the reliability of the algorithm.

Obviously, those skilled in the art should understand that each module or each step of the above-mentioned embodiments of the present invention can be implemented by a general-purpose computing device, and they can be concentrated on a single computing device, or distributed among multiple computing devices. Optionally, they may be implemented in program code executable by a computing device, thereby, they may be stored in a storage device to be executed by a computing device, and in some cases, may be implemented in a code different from that described herein The steps shown or described are executed in sequence, or they are fabricated into individual integrated circuit modules, or multiple modules or steps among them are fabricated into a single integrated circuit module for implementation. Thus, embodiments of the invention are not limited to any specific combination of hardware and software.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, various modifications and changes may be made to the embodiments of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (8)

1. A voltage stability analysis method of a wind farm power system, characterized in that, comprising: Select the continuous parameter to form a new equation, use the new equation to expand the power flow equation of the power system, modify the power flow equation of the expanded power system, and obtain the revised power flow equation of the power system, in the revised power system In the power flow equation of , the modified power flow Jacobian matrix is the power flow Jacobian matrix when the node with the largest drop in voltage amplitude in the power system is treated as a node with specified injected power and voltage amplitude; Using the Newton-Raphson method to iteratively solve the power flow equation of the modified power system to obtain the predicted direction; Determine a prediction point according to the prediction direction and a preset step size; According to the prediction points, the voltage stability of the wind farm power system is analyzed. 2. the voltage stability analysis method of wind farm power system as claimed in claim 1 is characterized in that, the power flow equation of the power system after the correction is: ${\mathrm{<span\; class="notranslate">\; J</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&Delta;x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right]$ Among them, x is the state vector; f(x) is the power flow balance equation, and k is the row number; $J^{\&prime;\&prime;}=\left[\begin{array}{cc}{f}_x^{\&prime;}& b^{\&prime;}\\ f_{x^{\&prime;}}^T& b_k\end{array}\right],$ J″ is the Jacobian matrix of the modified extended power flow equation; f _x ′ is the modified Jacobian matrix of the power flow; b′ is the direction of load growth after modification; b _k is the kth element of b; x′ is the modified f'(x) is the revised power flow equation system; f _k (x) is the kth element of the vector function f(x); f _kx' is the function f _k (x) to x' Gradient vector; Δx' is the change vector corresponding to x', and Δλ is the change amount of wind power output level λ. 3. The voltage stability analysis method of the wind farm electric power system as claimed in claim 1, is characterized in that, adopts Newton-Raphson method to iteratively solve the power flow equation of the power system after the correction, comprising: After the current power flow calculation, the power flow solution for the next power flow calculation is predicted by the following formula, and the predicted power flow solution is used as the initial value of the next power flow calculation: $\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}& \mathrm{<span\; class="notranslate">\; b</span>}\\ {{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$ Among them, t _k is a column vector whose kth element is 1 and the rest are 0; b is the direction of load growth; f _x is the Jacobian matrix of the power flow equation of the power system; Δλ is the variation of wind power output level λ, Δx is the state change vector, Δx _k is the kth row element of Δx, and Δx _k is regarded as a constant. 4. The voltage stability analysis method of the wind farm power system according to any one of claims 1 to 3, wherein the preset step size is calculated by the following formula: $\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; /</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$ Wherein, h is a preset step size; h _max is a constant; y _i is the i-th component of the prediction direction y, and n is a positive integer. 5. A voltage stability analysis device for a wind farm power system, characterized in that it comprises: The equation extension correction module is used to select continuous parameters to form a new equation, use the new equation to expand the power flow equation of the power system, and correct the power flow equation of the extended power system to obtain the revised power flow equation of the power system , in the revised power flow equation of the power system, the revised power flow Jacobian matrix is the power flow Jacobian matrix when the node in the power system with the largest drop in voltage amplitude is treated as a node with specified injected power and voltage amplitude ; A solving module is used to iteratively solve the power flow equation of the revised power system by using the Newton-Raphson method to obtain the predicted direction; A determination module, configured to determine a prediction point according to the prediction direction and a preset step size; An analysis module, configured to analyze the voltage stability of the wind farm power system according to the prediction points. 6. The voltage stability analysis device of wind farm power system as claimed in claim 5, is characterized in that, the power flow equation of the power system after the correction is: ${\mathrm{<span\; class="notranslate">\; J</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&Delta;x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;b</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right]$ Among them, x is the state vector, f(x) is the power flow balance equation, and k is the row number; $J^{\&prime;\&prime;}=\left[\begin{array}{cc}{f}_x^{\&prime;}& b^{\&prime;}\\ f_{x^{\&prime;}}^T& b_k\end{array}\right],$ J″ is the modified Jacobian matrix of the power flow equation of the extended power system; f _x ′ is the modified Jacobian matrix of the power flow; b′ is the modified load growth direction b; b _k is the kth element of b ; x' is the corrected vector; f'(x) is the revised power flow equation; f _k (x) is the kth element of the vector function f(x); f _kx' is the function f _k (x) Gradient vector to x';Δx' is the change vector corresponding to x', and Δλ is the change amount of wind power output level λ. 7. The voltage stability analysis device of the wind farm power system as claimed in claim 5, wherein the solution module is specifically used for predicting the power flow solution of the next power flow calculation by the following formula after the current power flow calculation, and Use the predicted power flow solution as the initial value for the next power flow calculation: $\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}& \mathrm{<span\; class="notranslate">\; b</span>}\\ {{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$ Among them, t _k is a column vector whose kth element is 1 and the rest are 0; b is the direction of load growth; f _x is the Jacobian matrix of the power flow equation of the power system; Δλ is the variation of wind power output level λ; Δx is the state change vector; Δx _k is the k-th row element of Δx, and Δx _k is regarded as a constant. 8. The voltage stability analysis device of the wind farm power system according to any one of claims 5 to 7, further comprising: A step size calculation module, configured to calculate the preset step size by the following formula: $\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; /</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$ Wherein, h is a preset step size; h _max is a constant; y _i is the i-th component of the prediction direction y, and n is a positive integer.