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

Voltage stability analysis method and device for wind power plant 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 power plant electric power system.

Background

The reactive power characteristic of the wind farm is related to the active power characteristic of the wind farm. When the active output of the wind power plant is low, the power transmission line is lightly loaded, the line is charged with excessive reactive power, and the wind generating set is required to absorb the reactive power. If the reactive power absorbed by the wind generating set is insufficient, the wind farm will inject reactive power into the grid, and a high voltage problem may occur. When the active power output of the wind power plant is increased, the transmission line is overloaded, the consumed inductive reactive power is increased, the charging reactive power of the line is not enough to offset the inductive reactive power consumed by elements such as the line, a main transformer and the like, and the wind generating set is required to generate reactive power. If the reactive power generated by the wind generating set is insufficient, the wind power plant absorbs reactive power from the power grid. If the wind farm absorbs reactive power from the grid, a voltage sag in the wind farm may be caused. Therefore, when the power grid is insufficient in reactive power, and the wind turbine generator has large or full power output, a voltage stability problem may exist, and a detailed voltage stability analysis is necessary.

The continuous power flow method is one of basic methods for voltage stability analysis, ensures the convergence of power flow calculation at a critical point and nearby by selecting certain continuous parameters, and introduces mechanisms such as prediction, correction, step length adjustment and the like to reduce the iteration times required by the calculation process as much as possible and reduce the calculation amount. The method iterates repeatedly at each point of the lambda-V curve to calculate the accurate tide, so that the accurate information of the lambda-V curve and the like can be obtained, certain nonlinear control and inequality constraint conditions can be considered, and the method has strong robustness.

The existing continuous power flow method generally adds an equation on the basis of a basic equation of the continuous power flow, and simultaneously takes lambda as a variable, so that a row and a column are added to the right lower part of a Jacobian matrix, and the expanded Jacobian matrix is still in good state even at a critical point; however, the upper left corner of the power grid is still singular at the critical point, so that the convergence of the continuous power flow calculation near the critical point is difficult to be effectively ensured, the reliability of the algorithm is greatly influenced, and the reliability of the voltage stability analysis of the power system of the wind power plant is further influenced.

Disclosure of Invention

The embodiment of the invention provides a voltage stability analysis method for a wind power plant power system, and aims to solve the technical problems that in the prior art, the convergence of continuous power flow calculation near a critical point is difficult to be effectively ensured, and the reliability of an algorithm is greatly influenced. The method comprises the following steps: selecting continuous parameters to form a new equation, expanding a power flow equation of the power system by using the new equation, and correcting the expanded power flow equation of the power system to obtain a corrected power flow equation of the power system, wherein in the corrected power flow equation of the power system, a corrected power flow jacobian matrix is a power flow jacobian matrix when a node with the maximum voltage amplitude reduction in the power system is treated as a node designated by both injection power and voltage amplitude; iteratively solving the power flow equation of the corrected power system by adopting a Newton-Raphson method to obtain a prediction direction; determining a prediction point according to the prediction direction and a preset step length; and analyzing the voltage stabilization condition of the power system of the wind power plant according to the prediction point.

In one embodiment, the modified power flow equation of the 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 a state vector; (x) is the power flow balance equation, k is the line number; $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ j' is a Jacobian matrix of the modified extended power flow equation; f'_xIs a corrected power flow jacobian matrix; b' is the corrected load growth direction; b_kThe kth element of b; x' is the corrected state vector; f' (x) is the corrected power flow equation set; f. of_k(x) Is the kth element of the vector function f (x); f. of_kx′As a function f_k(x) A gradient vector for x'; Δ x 'is a variation vector corresponding to x', and Δ λ is a variation amount of the wind power output level λ.

In one embodiment, iteratively solving the modified power flow equation of the power system by using a newton-raphson method includes: after the current power flow is calculated, predicting a power flow solution of the next power flow calculation through the following formula, and taking the predicted power flow solution as an initial value of the next power flow calculation:

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

wherein, t_kIs a column vector with the kth element being 1 and the remaining elements being 0; b is the direction of load growth; f. of_xIs a Jacobian matrix of a power flow equation of the power system; delta lambda is the variation of the wind power output level lambda, Delta x is the state variation vector, Delta x_kIs the k-th row element of Δ x, will Δ x_kAs constants.

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

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

wherein h is a preset step length; h is_maxIs a constant; y is_iTo predict the ith component of direction y, n is a positive integer.

The embodiment of the invention also provides a voltage stability analysis device of a wind power plant power system, which is used for solving the technical problems that the convergence of the continuous power flow calculation near the critical point is difficult to be effectively ensured and the reliability of the algorithm is greatly influenced in the prior art. The device includes: the equation expansion and correction module is used for selecting the continuous parameters to form a new equation, expanding the power flow equation of the power system by using the new equation, correcting the power flow equation of the expanded power system to obtain a corrected power flow equation of the power system, and in the corrected power flow equation of the power system, the corrected power flow Jacobian matrix is a power flow Jacobian matrix when a node with the maximum voltage amplitude reduction in the power system is used as a node designated by both injection power and voltage amplitude to be processed; the solving module is used for iteratively solving the corrected power flow equation of the power system by adopting a Newton-Raphson method to obtain a prediction direction; the determining module is used for determining a prediction point according to the prediction direction and a preset step length; and the analysis module is used for analyzing the voltage stability condition of the power system of the wind power plant according to the prediction point.

In one embodiment, the modified power flow equation of the 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 a state vector, f (x) is a power flow balance equation, and k is a line number; $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ j' is a Jacobian matrix of the modified power flow equation of the extended power system; f'_xIs a corrected power flow jacobian matrix; b' is the corrected load growth direction b; b_kThe kth element of b; x' is the corrected vector; f' (x) is the corrected power flow equation set; f. of_k(x) Is the kth element of the vector function f (x); f. of_kx′As a function f_k(x) A gradient vector for x'; Δ x 'is a variation vector corresponding to x', and Δ λ is a variation amount of the wind power output level λ.

In an embodiment, the solving module is specifically configured to, after the current power flow calculation, predict a power flow solution of a next power flow calculation by using the following formula, and use the predicted power flow solution as an initial value of the next power flow calculation:

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

wherein, t_kIs a column vector with the kth element being 1 and the remaining elements being 0; b is the direction of load growth; f. of_xIs a Jacobian matrix of a power flow equation of the power system; Δ λ is the variation of the wind power output level λ; Δ x is a state change vector; Δ x_kIs the k-th row element of Δ x, will Δ x_kAs constants.

In one embodiment, further comprising: the step length calculating module is used for calculating the preset step length through the following formula:

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

wherein h is a preset step length; h is_maxIs a constant; y is_iTo predictThe ith component of direction y, n is a positive integer.

In the embodiment of the 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 which can be solved by a fixed value, the expanded power flow equation of the power system is corrected, so that the corrected power flow Jacobian matrix is a power flow Jacobian matrix when the weakest node (namely the node with the largest voltage amplitude value reduction) in the power system is treated as a PV node (namely the node appointed by both injection power and voltage amplitude value), namely the Jacobian matrix of the power flow equation of the corrected power system is nonsingular at and near a critical point, and the corrected Jacobian matrix (namely the upper left corner part matrix of the power flow equation of the corrected power system) is nonsingular at and near the critical point, thereby solving the singular problem at the critical point of the left corner part matrix (namely the power flow Jacobian matrix of the power flow) of the expanded power flow matrix, the method overcomes the adverse effect on numerical calculation caused by singularity and nearby morbidity of the critical point of the tidal current Jacobian matrix, the calculation precision of the extended correction equation can be effectively ensured, the convergence of continuous tidal current calculation nearby the critical point is greatly improved, and the reliability of the algorithm is improved.

Drawings

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:

FIG. 1 is a flowchart of a voltage stability analysis method for a wind farm power system according to an embodiment of the present invention;

FIG. 2 is a schematic diagram illustrating a point-by-point calculation method according to an embodiment of the present invention;

FIG. 3 is a schematic diagram illustrating an arc length continuous process provided by an embodiment of the present invention;

FIG. 4 is a schematic illustration of a homotopic continuous process provided by an embodiment of the present invention;

FIG. 5 is a schematic diagram illustrating a local parameter continuity method provided by an embodiment of the present invention;

FIG. 6 is a schematic diagram of a λ -V curve under consideration of reactive limiting according to an embodiment of the present invention;

FIG. 7 is a second schematic diagram of a λ -V curve considering reactive limiting according to an embodiment of the present invention;

FIG. 8 is a third schematic diagram of a λ -V curve considering reactive limiting according to an embodiment of the present invention;

fig. 9 is a block diagram of a voltage stability analysis device of a wind farm power system according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the following embodiments and accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.

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

step 101: selecting continuous parameters to form a new equation, expanding a power flow equation of the power system by using the new equation, and correcting the expanded power flow equation of the power system to obtain a corrected power flow equation of the power system, wherein in the corrected power flow equation of the power system, a corrected power flow jacobian matrix is a power flow jacobian matrix when a node with the maximum voltage amplitude reduction in the power system is treated as a node designated by both injection power and voltage amplitude;

step 102: iteratively solving the power flow equation of the corrected power system by adopting a Newton-Raphson method to obtain a prediction direction;

step 103: determining a prediction point according to the prediction direction and a preset step length;

step 104: and analyzing the voltage stabilization condition of the power system of the wind power plant according to the prediction point.

It can be known from the flow shown in fig. 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 be solved by a fixed value, and the power flow equation of the expanded power system is modified, so that the modified power flow jacobian matrix is a power flow jacobian matrix when the thinnest weak node (i.e., the node with the largest voltage amplitude reduction) in the power system is treated as a PV node (i.e., the node specified by both the injection power and the voltage amplitude), i.e., the jacobian matrix of the power flow equation of the modified power system is nonsingular at and near the critical point, and the modified power flow jacobian matrix (i.e., the upper left-corner partial matrix of the power flow equation of the modified power system) is nonsingular at and near the critical point, thereby solving the singular problem at the critical point of the upper-left-corner partial matrix (i.e., the power flow jacobian matrix) of the expanded power flow jacobian, the method overcomes the adverse effect on numerical calculation caused by singularity and nearby morbidity of the critical point of the tidal current Jacobian matrix, the calculation precision of the extended correction equation can be effectively ensured, the convergence of continuous tidal current calculation nearby the critical point is greatly improved, and the reliability of the algorithm is improved.

In specific implementation, because the power flow equation of the power system expanded by the new equation is an equation capable of obtaining a fixed value solution, and the expanded jacobian matrix is nonsingular at the critical point, but the upper left-hand partial matrix (i.e., the conventional power flow jacobian matrix) of the expanded jacobian matrix is singular at the critical point, and the critical point is in a sick state, the calculation accuracy of the expanded power flow equation at and near the critical point is difficult to be effectively guaranteed, and the convergence of the continuous power flow method at and near the critical point cannot be effectively guaranteed, in order to realize that the upper left-hand partial matrix (i.e., the conventional power flow jacobian matrix) of the expanded jacobian matrix is nonsingular at the critical point, in this embodiment, the power flow equation of the expanded power system is modified to obtain the modified power flow equation of the power system:

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

wherein x is a state vector, i.e., a vector consisting of the voltage amplitude and phase of each node; (x) is the power flow balance equation, k is the line number; $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ j' is a Jacobian matrix of the modified power flow equation of the extended power system; f'_xThe modified power flow Jacobian matrix is the remaining matrix after the k row and the k column of the power flow Jacobian matrix are scratched; b' is the modified load growth direction b, namely the residual vector of the k line after b is scratched; b_kThe kth element of b; x' is the corrected vector x, namely the residual vector after the line k is scratched by x; f' (x) is a corrected power flow equation set, namely a residual vector after the k line is cut out of a function vector f (x); f. of_k(x) Is the kth element of the vector function f (x); f. of_kx′As a function f_k(x) A gradient vector for x'; Δ x 'is a variation vector corresponding to x', and Δ λ is a variation amount of the wind power output level λ. Specifically, x is_kAs a constant and using equation f_k(x)+λb_kMoving to the last row, 0, it can be seen that,j ' is actually J ' (i.e., a Jacobian matrix of a power flow equation of an expanded power system) obtained by dividing line n +1 by line k and then shifting line k to the last line f '_xIs a conventional trend jacobian matrix f_xScratching out the matrix of the kth row and the kth column; b' is the vector of the k-th element of the vector b; b_kIs the kth element of vector b; x' is the vector after the k element is cut off from the vector x; f' (x) is the vector after the k element is cut out by the vector function f (x); f. of_k(x) Is the kth element of the vector function f (x); f. of_kx′As a function f_k(x) For the gradient vector of x'.

In specific implementation, the continuous power flow calculation adopts a Newton-Raphson method to solve an extended power flow equation. After each load flow calculation, if the next load flow solution is predicted and the predicted load flow solution is taken as the initial value of the next load flow calculation, the iteration times of the load flow calculation can be obviously greatly reduced, and the calculation speed is accelerated. In order to improve the success rate of prediction and improve the accuracy and robustness of the prediction process, in this embodiment, a newton-raphson method is used to iteratively solve the modified power flow equation of the power system, including: after the current power flow is calculated, predicting a power flow solution of the next power flow calculation through the following formula, and taking the predicted power flow solution as an initial value of the next power flow calculation:

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

wherein, t_kIs a column vector with the kth element being 1 and the remaining elements being 0; b is the direction of load growth; f. of_xIs a Jacobian matrix of a power flow equation of the power system; delta lambda is the variation of the wind power output level lambda, Delta x is the state variation vector, Delta x_kIs the k-th row element of Δ x, will Δ x_kAs a constant, let Δ x_kAs constants, i.e. stroke-out formulas $\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right]=\left[\begin{array}{c}0\\ -1\end{array}\right]$ And f is the last row of_xThe k-th column of the equation is shifted to the right end term, then the k-th line of the equation is shifted to the last line, and the prediction direction y can be obtained by solving the equation.

In specific implementation, after a prediction direction is given, a step length h needs to be given to determine a prediction point. The choice of the step size has a significant impact on the performance of the continuous flow method. The step length is too small, each load flow calculation can be converged quickly, but the calculation can be carried out to the vicinity of the critical point after many times of calculation, and the required times are more if the lower half branch of the lambda-V curve is calculated. The step length is too large, the distance between the predicted point and the required point is possibly far, the iteration number required by each load flow calculation is more, the result may cost more calculation time, and even the continuous load flow calculation may not be converged. In general, the basic principle of step size selection is that in the portion where the curve is relatively flat, the step size takes a larger value; the smaller the curve is in the more curved portion. Therefore, in the present embodiment, the preset step size is calculated by the following formula:

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

wherein h is a preset step length; h is_maxIs a constant; y is_iTo predict the ith component of direction y, n is a positive integer. Specifically, a variable-step concept can be introduced into the continuous power flow calculation, if the number of iterations required by the continuous power flow calculation is large, the step size is reduced, if the number of iterations is small, the step size is increased, and if the number of iterations is moderate, the original step size is maintained.

The voltage stability analysis method of the wind farm power system is described below with reference to specific examples. For example:

the basic power flow equation of the power system is as follows:

f(x)+λb＝0(1)

wherein, x ∈ RⁿF (x) is a vector of n-dimensional function, b is the direction of load growth, b ∈ Rⁿ(ii) a λ is an actual parameter which, physically speaking, actually represents to some extent the load level of the system.

The basic power flow equation of the formula (1) has n +1 variables, but only n equations cannot solve a constant value solution, and actually is a curve on a n +1 dimensional space. To solve the fixed value, an equation must be added. The simplest and most intuitive method is to use the point-by-point calculation method shown in fig. 2, and determine the value of λ in each load flow calculation, and then obtain the corresponding fixed value solution. However, when λ takes a certain large value, the correction equation may be ill-conditioned, and as the λ value continues to increase, the ill-conditioned will become more serious, and when λ is large to a certain extent, the ill-conditioned of the correction equation will make the conventional power flow calculation unable to converge. This is intuitively illustrated by the point-by-point calculation illustrative diagram of fig. 2. As the load level increases, the lambda value increases and the point x is predicted_pTo the right when x_pWhen x is tangent to the lambda-V curve, x is the voltage collapse critical point, but because the Jacobian matrix is singular at the critical point and is ill-conditioned near the critical point, the load flow calculation cannot be converged, and the numerical calculation fails. To overcome this drawback, the continuous tidal current method is in use.

The key of the continuous power flow method is to select reasonable continuous parameters to ensure the convergence of the critical point and the vicinity thereof. At present, the continuous parameter method mainly includes an arc length continuous method, a homological continuous method and a local parameter continuous method.

FIG. 3 shows the basic concept of the arc length continuity method, which is based on the idea that the parameter S is introduced to represent the distance from x to the initial point x₀And takes S equal to x₀x_pIs realized, namely the newly added equation is as follows:

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

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

FIG. 4 shows the basic concept of homotopy continuity method, which is based on the concept of vector x-x_pAnd vector x₀-x_pVertical, whereby the equation (i.e., the new equation above) can be added:

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

fig. 5 illustrates visually the basic concept of the local parameter continuity method. The basic idea is to determine some element of the vector x according to the prediction direction, i.e. according to x₀And x_pAdd equation (i.e., the new equation above):

x_k＝x_pk(4)

wherein k is a subscript corresponding to the local continuous parameter, and the vector x is generally taken in practice_p-x₀The subscript corresponding to the element with the maximum absolute value can limit k to the element corresponding to the voltage for continuous power flow calculation.

After the processing, the expanded power flow equation has n +1 equations and n +1 variables, so that a constant value solution can be obtained.

For convenience of explanation, the equations added above (i.e., the new equations above) are collectively expressed by g (x, λ) ═ 0. Solving the extended power flow equation by using a Newton-Raphson method, wherein the corresponding extended power flow equation 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_xj' 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 (i.e., a saddle junction 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 of the formula (5), since the extended power flow jacobian matrix J' is not singular at the critical point, the method can reliably calculate to the voltage collapse critical point if the principal elements are triangulated. However, for sparsity, the Jacobian matrix triangle decomposition usually does not select principal element, and J' top left corner partial matrix f_xThe conventional tidal current Jacobian matrix is singular at the critical point and is ill-conditioned near the critical point, so that the calculation accuracy of the expansion equation at and near the critical point is difficult to effectively guarantee, and the convergence of the continuous tidal current method at and near the critical point can also not be effectively guaranteed.

To overcome the above disadvantages, the algorithm implementation of the local parameter continuum method is modified appropriately. Iteratively solving lambda-V curve and newly added equation x_k＝x_pkIn the process of crossing point of (a), x is not added_k＝x_pkConsidered as an equation, but will be x_kAs a constant and using equation f_k(x)+λb_kMove to the last row for 0. Correspondingly, the modified equation (i.e. the power flow equation of the modified power system) corresponding to the newton-raphson method is iteratively solved 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 the corrected power flow Jacobian matrix; f'_xIs f_xScratching out the matrix of the kth row and the kth column; b' is the vector of the k-th element of the vector b; b_kIs the kth element of vector b; x' is the vector after the k element is cut off from the vector x; f' (x) is the vector after the k element is cut out by the vector function f (x); f. of_k(x)Is the kth element of the vector function f (x); f. of_kx′As a function f_k(x) For the gradient vector of x'.

It can be seen that J 'is actually the result of J' scratching out row n +1 and column k and moving row k to the last row.

For the local parametric continuum method, in equation (5)Now assuming J' is singular at the critical point, thenSuch that J "w" is 0. Construct vector w ═ w₁,w₂,...,w_k-1,0,w_k,...,w_n)^TThen J 'w' is 0. Since w '≠ 0, it can be obtained from w ≠ 0, so that J' has singularity. This contradicts the non-singularity of J' at the normal inflection point, which demonstrates that J "is non-singularity at the critical point if the critical point is a normal inflection point.

For the continuous power flow calculation of the power system, at the voltage collapse critical point and the vicinity thereof, x is selected according to the selection principle of the subscript k_kShould correspond to the voltage of the node with the fastest voltage drop, indicating f'_xIs the flow Jacobian matrix when the weakest node of the system is treated as a PV node. From a physical point of view, treating a node as a PV node actually means that the node voltage remains constant. Conceivably, if sufficient reactive power is placed at a weak node of the system to maintain the node voltage constant, the voltage stability margin of the system must increase, which means f'_xThe critical point is not singular. It can be seen that, even at the critical point, f'_xAnd J' are all nonsingular, the continuous power flow method can reliably calculate the voltage collapse critical point.

From the perspective of space analytic geometry, each point of continuous power flow calculation is equivalent to solving the intersection point of the lambda-V curve and the space curved surface corresponding to the newly added equation. And (3) iteratively solving the intersection point of a curve and a curved surface in the multidimensional space by using a Newton-Raphson method, wherein when the curve is tangent to the curved surface, the corresponding Jacobian matrix is singular, the numerical calculation cannot be converged, the convergence is the best when the curve is orthogonal, and the convergence is between the two when the curve is intersected. The singularities at the critical points of the jacobian matrix of the tidal current equation are derived from the tangency of the lambda-V curve and the lambda-constant surface. For the continuous power flow method, the space curved surface corresponding to the newly added equation is not tangent to the lambda-V curve any more but is intersected with the lambda-V curve, so that the expanded power flow Jacobian matrix is not singular any more.

As the previous continuous power flow methods do not solve the ill condition of the upper left corner partial matrix of the extended power flow jacobian matrix caused by the ill condition near the critical point of the conventional power flow jacobian matrix, the calculation accuracy of the extended correction equation near the critical point is influenced, and the convergence of the continuous power flow calculation cannot be effectively ensured. By adopting the method, the singularity at the critical point of the upper left corner part of the extended power flow Jacobian matrix is solved, the calculation precision of the extended correction equation can be effectively ensured, and the convergence of the continuous power flow calculation near the critical point is greatly improved. In fact, for a two-dimensional system, the spatial curved surface corresponding to the new-added equation of the local parameter continuity method is orthogonal to the lambda-V curve at the critical point, and through the improvement of the project, the calculation accuracy of the extended correction equation can be effectively ensured, and the convergence near the critical point of the extended correction equation is better than that of other points. For high-dimensional systems, the above properties are not always present, but are generally regular. Of course, the nature of the Jacobian matrix is not the only factor determining the convergence rate of the algorithm, the Newton-Raphson method is adopted to carry out numerical solution on the nonlinear equation set, and the convergence performance of the algorithm is closely related to the initial value.

The continuous power flow calculation is generally used for solving an extended power flow equation by a Newton-Raphson method. After each load flow calculation, if the next load flow solution is predicted and used as the initial value of the next load flow calculation, the iteration times of the load flow calculation can be obviously greatly reduced, and the calculation speed is accelerated.

The essence of the tangent method is to predict the next power flow solution using the differential of the current solution. The full differentiation is carried out on the basic equation of the continuous power flow in the formula (1) to obtain:

f_xdx+bdλ＝0(7)

let the predicted direction be $y=\left(\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}\mathrm{\λ}\end{array}\right),$ Then there is

f_xΔx+bΔλ＝0(8)

If f_x ^TIs good, let Δ λ equal to 1, then

f_xΔx＝-b(9)

Directly solving the equation to obtain delta x, namely obtaining the prediction direction $y=\left(\begin{array}{c}\mathrm{\Δ}x\\ 1\end{array}\right).$

For the initial point of the continuous power flow calculation, the jacobian matrix is good state only because of the current point information, so the method is generally directly adopted for prediction.

However, the tidal current jacobian matrix is singular at the critical point and ill-conditioned near the critical point, so that the solving precision of the matrix equation of the formula (9) at and near the critical point cannot be effectively guaranteed, and the prediction effect may be poor.

For formula (8), let Δ x_k＝-1，1≤k≤nThen, there is a formula for predicting the load flow solution of the next load flow calculation:

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

wherein, t_kIs a column vector with the k-th element being 1 and the remaining elements being 0, i.e.

For the convenience of the following explanation, the following reasoning is given.

Introduction 1: for matrix $M=\left[\begin{array}{cc}A& b\\ c& d\end{array}\right],$ When a is singular and dimnull (a) is 1, if and only if $b\∉Range\left(A\right),c^T\∉Range\left(A^T\right)$ When M is not singular.

If the critical point is a normal inflection point, then the critical point is dimnull (f)_x) 1, andnow suppose f_xScratch out the remaining matrix f 'after the k line and k column'_xIs in good condition, then there areFrom lemma 1, the matrix $\left[\begin{array}{cc}{f}_x& b\\ {t_k}^T& 0\end{array}\right]$ Is not unusual.

From the above section, if k is an element corresponding to a weak node voltage, f'_xThe method is good, so that the weak node of the system is determined only by analyzing the last prediction direction or sensitivity, the subscript k is selected accordingly, and then the equation (10) is solved directly, so that the prediction direction y can be obtained, namely, the tangent prediction method.

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

Will be Δ x_kAs constants, i.e. scratch out the last row of equation (10) and divide f_xThe k-th column of the equation is shifted to the right end term, then the k-th line of the equation is shifted to the last line, and the prediction direction y can be obtained by solving the equation.

Through the processing, the prediction process effectively overcomes the prediction failure possibly caused by singularity of the tidal current Jacobian matrix at the critical point and unsmooth of a lambda-V curve before and after node type conversion, and the precision and the robustness of the prediction process are greatly improved.

After the prediction direction is given, the step length h needs to be given to determine the prediction point. The step size selection has an important influence on the performance of the continuous flow method. The step length is too small, each load flow calculation can be converged quickly, but the calculation can be carried out to the vicinity of the critical point after many times of calculation, and the required times are more if the lower half branch of the lambda-V curve is calculated. The step length is too large, the distance between the predicted point and the required point is possibly far, the iteration number required by each load flow calculation is more, the result may cost more calculation time, and even the continuous load flow calculation may not be converged.

In general, the basic principle of step size selectionThe step length is a larger value at the part where the curve is relatively flat; the smaller the curve is in the more curved portion. Here getWherein h is_maxIs a given constant, y_iIs the i-th component of the prediction direction y. Obviously, this method satisfies the basic principles described above. Simulation calculation also proves the effectiveness of the method.

In addition, a variable step length concept can be introduced into the continuous power flow calculation, if the number of iterations required by the continuous power flow calculation is large, the step length is reduced, if the number of iterations required by the continuous power flow calculation is small, the step length is increased, and if the number of iterations is moderate, the original step length is kept.

The ability of the generator to maintain the terminal voltage greatly affects the voltage stability of the power system. In practical power systems, the generator is limited by the maximum field current and winding heating conditions, and its reactive power output is limited. It is assumed here that the maximum reactive power contribution will remain unchanged as soon as the generator reactive power contribution reaches its upper limit. From the point of view of load flow calculation, this is the conversion of the generator from the PV node to the PQ node. The reactive power output limit of the generator is one of the most important nonlinear factors in the static voltage stability research, and whether the reactive power output limit of the generator directly influences the rationality of the critical point calculation is considered. If the reactive power output limit of the generator is not considered, the calculation result is biased to be optimistic.

The state index method only calculates the current state, so the reactive power output limit of the generator can not be considered generally. For the continuous flow method, this factor must be taken into account.

Fig. 6 to 8 show the conversion from PV node to PQ node (Q ═ Q) after the reactive power of a certain generator reaches the upper limit^max) Three possible variations of the time λ -V curve. Wherein curve I is a lambda-V curve when the generator is treated as a PV node, curve II is a lambda-V curve when the generator is treated as a PQ node, and the solid line portion is the actual lambda-V curve when the reactive power limit of the generator is considered.

As can be seen from fig. 6-8, the actual lambda-V curve will be continuous rather than smooth when the generator is converted from the PV node to the PQ node.

For the case of fig. 6, the two λ -V curves meet at the respective upper half branches, and their actual critical points are those at which the generator is treated as a PQ node. In the case of fig. 7 and 8, the intersection point between the upper half branch of the curve I and the lower half branch of the curve II is actually the voltage collapse critical point, and therefore, the intersection point should be obtained when the continuous current calculation is performed. Fig. 8 is similar in nature to fig. 7, except for two different situations that may arise due to the multiplicity of the power flow.

If a linear prediction method is adopted for prediction, for the situation of fig. 6, because the gradient change of the actual lambda-V curve on the two sides of the turning point is not very large, the distance between the prediction point and the actual lambda-V curve is not very long in general, the convergence of the algorithm can still be ensured, and only the required iteration times may be relatively large; for the situation of fig. 7, the gradient change on both sides of the turning point is large, the prediction point may be far away from the actual λ -V curve, the iteration number required by the continuous power flow calculation is generally large, and even the continuous power flow calculation may not be converged; for the case of fig. 8, it may not converge or even converge to the wrong branch.

The analysis shows that when the reactive power output limit of the generator is considered, if a linear prediction method is adopted, the reactive power output of the continuous power flow calculation is limited, and when the node type of the end node is converted, a tangent prediction method is adopted for prediction, so that the complexity of the algorithm is undoubtedly increased. Of course, if the generator reactive power output limit is not considered, a linear prediction method may be employed.

Based on the same inventive concept, the embodiment of the invention also provides a voltage stability analysis device of a wind power plant power system, as described in the following embodiments. Because the principle of solving the problems of the voltage stability analysis device of the wind power plant power system is similar to the voltage stability analysis method of the wind power plant power system, the implementation of the voltage stability analysis device of the wind power plant power system can refer to the implementation of the voltage stability analysis method of the wind power plant power system, and repeated parts are not repeated. As used hereinafter, the term "unit" or "module" may be a combination of software and/or hardware that implements a predetermined function. Although the means described in the embodiments below are preferably implemented in software, an implementation in hardware, or a combination of software and hardware is also possible and contemplated.

Fig. 9 is a block diagram of a structure of a voltage stability analysis device of a wind farm power system according to an embodiment of the present invention, and as shown in fig. 9, the voltage stability analysis device includes: an equation expansion modification module 901, a solving module 902, a determining module 903 and an analyzing module 904, and the structure is explained below.

An equation expansion and correction module 901, configured to select the continuity parameters to form a new equation, expand the power flow equation of the power system using the new equation, and correct the power flow equation of the expanded power system to obtain a corrected power flow equation of the power system, where in the corrected power flow equation of the power system, the corrected power flow jacobian matrix is a power flow jacobian matrix when a node in the power system where a voltage amplitude value is decreased most is treated as a node designated by both injection power and a voltage amplitude value;

the solving module 902 is connected with the equation expansion and correction module 901 and is used for iteratively solving the power flow equation of the corrected power system by adopting a Newton-Raphson method to obtain a prediction direction;

a determining module 903, connected to the solving module 902, for determining a predicted point according to the predicted direction and a preset step length;

and the analysis module 904 is connected with the determination module 903 and is used for analyzing the voltage stabilization condition of the power system of the wind power plant according to the predicted point.

In one embodiment, the modified power flow equation of the 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 a state vector, f (x) is a power flow balance equation, and k is a line number; $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ j' is a Jacobian matrix of the modified power flow equation of the extended power system; f'_xIs a corrected power flow jacobian matrix; b' is the corrected load growth direction b; b_kThe kth element of b; x' is the corrected vector x; f' (x) is the corrected power flow equation set; f. of_k(x) Is the kth element of the vector function f (x); f. of_kx′As a function f_k(x) A gradient vector for x'; Δ x 'is a variation vector corresponding to x', and Δ λ is a variation amount of the wind power output level λ.

In an embodiment, the solving module is specifically configured to, after the current power flow calculation, predict a power flow solution of a next power flow calculation by using the following formula, and use the predicted power flow solution as an initial value of the next power flow calculation:

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

wherein, t_kIs a column vector with the kth element being 1 and the remaining elements being 0; b is the direction of load growth; f. of_xIs a Jacobian matrix of a power flow equation of the power system; Δ λ is the variation of the wind power output level λ; Δ x is a state change vector; Δ x_kIs the k-th row element of Δ x, will Δ x_kAs constants.

In one embodiment, further comprising: the step length calculating module is used for calculating the preset step length through the following formula:

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

wherein h is a preset step length; h is_maxIs a constant; y is_iTo predict the ith component of direction y, n is a positive integer.

In the embodiment of the invention, the new equation is used for expanding the power flow equation of the power system, the expanded power flow equation is an equation which can be solved with a fixed value, the expanded power flow equation of the power system is corrected, the corrected power flow Jacobian matrix is a power flow Jacobian matrix when the weakest node in the power system is taken as a PV node for processing, namely the Jacobian matrix of the power flow equation of the corrected power system is nonsingular at and near the critical point, and the corrected power flow Jacobian matrix (namely the upper left corner part matrix of the Jacobian matrix of the power flow equation of the corrected power system) is nonsingular at and near the critical point, so that the singular problem at the critical point of the upper left corner part matrix of the expanded power flow Jacobian matrix (namely the power flow Jacobian matrix) is solved, and the bad influence of singular at and near the critical point of the power flow matrix on numerical calculation caused by the singular and the ill condition thereof is overcome, the calculation accuracy of the extended correction equation can be effectively guaranteed, the convergence of the continuous power flow calculation near the critical point is greatly improved, and the reliability of the algorithm is improved.

It will be apparent to those skilled in the art that the modules or steps of the embodiments of the invention described above may be implemented by a general purpose computing device, they may be centralized on a single computing device or distributed across a network of multiple computing devices, and alternatively, they may be implemented by program code executable by a computing device, such that they may be stored in a storage device and executed by a computing device, and in some cases, the steps shown or described may be performed in an order different than that described herein, or they may be separately fabricated into individual integrated circuit modules, or multiple ones of them may be fabricated into a single integrated circuit module. Thus, embodiments of the invention are not limited to any specific combination of hardware and software.

The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made to the embodiment of the present invention by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (8)

1. A voltage stability analysis method of a wind power plant power system is characterized by comprising the following steps:

selecting continuous parameters to form a new equation, expanding a power flow equation of the power system by using the new equation, and correcting the expanded power flow equation of the power system to obtain a corrected power flow equation of the power system, wherein in the corrected power flow equation of the power system, a corrected power flow jacobian matrix is a power flow jacobian matrix when a node with the maximum voltage amplitude reduction in the power system is treated as a node designated by both injection power and voltage amplitude;

iteratively solving the power flow equation of the corrected power system by adopting a Newton-Raphson method to obtain a prediction direction;

determining a prediction point according to the prediction direction and a preset step length;

and analyzing the voltage stabilization condition of the power system of the wind power plant according to the prediction point.

2. The voltage stability analysis method of a wind farm power system according to claim 1, characterized in that the power flow equation of the modified 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 a state vector; (x) is the power flow balance equation, k is the line number; $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ j' is a Jacobian matrix of the modified extended power flow equation; f. of_x' is a corrected power flow jacobian matrix; b' is the corrected load growth direction; b_kThe kth element of b; x' is the corrected state vector; f' (x) is the corrected power flow equation set; f. of_k(x) Is the kth element of the vector function f (x); f. of_kx′As a function f_k(x) A gradient vector for x'; Δ x 'is a variation vector corresponding to x', and Δ λ is a variation amount of the wind power output level λ.

3. The voltage stability analysis method of the wind farm power system according to claim 1, wherein the iterative solution of the power flow equation of the corrected power system by using a newton-raphson method comprises:

after the current power flow is calculated, predicting a power flow solution of the next power flow calculation through the following formula, and taking the predicted power flow solution as an initial value of the next power flow calculation:

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

wherein, t_kIs a column vector with the kth element being 1 and the remaining elements being 0; b is the direction of load growth; f. of_xIs a Jacobian matrix of a power flow equation of the power system; delta lambda is the variation of the wind power output level lambda, Delta x is the state variation vector, Delta x_kIs the k line element of Δ x, willΔx_kAs constants.

4. A voltage stability analysis method of a wind farm power system according to any of the claims 1 to 3, characterized in that said preset step size is calculated by the following formula:

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

wherein h is a preset step length; h is_maxIs a constant; y is_iTo predict the ith component of direction y, n is a positive integer.

5. A voltage stability analysis device of a wind power plant electric power system is characterized by comprising:

the equation expansion and correction module is used for selecting the continuous parameters to form a new equation, expanding the power flow equation of the power system by using the new equation, correcting the power flow equation of the expanded power system to obtain a corrected power flow equation of the power system, and in the corrected power flow equation of the power system, the corrected power flow Jacobian matrix is a power flow Jacobian matrix when a node with the maximum voltage amplitude reduction in the power system is used as a node designated by both injection power and voltage amplitude to be processed;

the solving module is used for iteratively solving the corrected power flow equation of the power system by adopting a Newton-Raphson method to obtain a prediction direction;

the determining module is used for determining a prediction point according to the prediction direction and a preset step length;

and the analysis module is used for analyzing the voltage stability condition of the power system of the wind power plant according to the prediction point.

6. The voltage stabilization analysis device of a wind farm power system according to claim 5, wherein the power flow equation of the modified 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 a state vector, f (x) is a power flow balance equation, and k is a line number; $J^{\′\′}=\left[\begin{array}{cc}{f}_x^{\′}& b^{\′}\\ f_{{\mathrm{kx}}^{\′}}^T& b_k\end{array}\right],$ j' is a Jacobian matrix of the modified power flow equation of the extended power system; f. of_x' is a corrected power flow jacobian matrix; b' is the corrected load growth direction b; b_kThe kth element of b; x' is the corrected vector; f' (x) is the corrected power flow equation set; f. of_k(x) Is the kth element of the vector function f (x); f. of_kx′As a function f_k(x) A gradient vector for x'; Δ x 'is a variation vector corresponding to x', and Δ λ is a variation amount of the wind power output level λ.

7. The voltage stability analysis device of the wind farm power system according to claim 5, wherein the solving module is specifically configured to predict a current solution of a next current calculation after the current calculation by using the following formula, and use the predicted current solution as an initial value of the next current calculation:

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

wherein, t_kIs a column vector with the kth element being 1 and the remaining elements being 0; b is the direction of load growth; f. of_xIs a Jacobian matrix of a power flow equation of the power system; Δ λ is the variation of the wind power output level λ; Δ x is a state change vector; Δ x_kIs the k-th row element of Δ x, will Δ x_kAs constants.

8. The voltage stabilization analysis device of a wind farm power system according to any one of claims 5 to 7, characterized by further comprising:

the step length calculating module is used for calculating the preset step length through the following formula:

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

wherein h is a preset step length; h is_maxIs a constant; y is_iTo predict the ith component of direction y, n is a positive integer.