CN116992776B - Voltage source converter stability domain construction method and system based on piecewise affine - Google Patents
Voltage source converter stability domain construction method and system based on piecewise affine Download PDFInfo
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Abstract
The invention belongs to the technical field of converters, and particularly relates to a voltage source converter stability domain construction method and system based on piecewise affine, wherein the method comprises the following steps: obtaining an impedance model of the voltage source converter; constructing a segmented affine impedance model of the voltage source converter based on the segmented affine and the acquired impedance model; solving the constructed piecewise affine impedance model to finish the construction of the stable domain of the voltage source converter; in the process of solving the constructed segmented affine impedance model, a double-layer optimization solving model is adopted, an inner layer model in the double-layer optimization solving model is combined with the constructed segmented affine impedance model and a Nyquist criterion to judge the stability of the working point in the small interference stable domain of the voltage source converter, the inner layer model is used as the nonlinear constraint of an outer layer model in the double-layer optimization solving model, so that the solving of the model is completed, and the construction of the stable domain of the voltage source converter is realized.
Description
Technical Field
The invention belongs to the technical field of converters, and particularly relates to a voltage source converter stability domain construction method and system based on piecewise affine.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
With the rapid development of new energy, the access of high-proportion power electronic equipment easily causes the problem of small disturbance instability, restricts the transportation and the absorption of the new energy, and seriously threatens the safe operation of a power system.
New energy oscillation accidents often result from small disturbance negative damping instability. The existing stability analysis method aiming at the problems mainly adopts a state space method and an impedance method; however, the designated working conditions need to be analyzed, and it is difficult to comprehensively evaluate the overall operation stability of the system, so that a method capable of reflecting the stability of all the working conditions of the system needs to be established. Due to the time-varying nature of the grid, the stability domain needs to be updated in time according to the changes in the grid parameters. There is therefore a need for a stable domain construction method that can meet the requirements of online applications. At present, the research on the new energy full-working-condition stable domain is less, and two main challenges exist: the new energy station model has high order and complex impedance calculation; secondly, the construction of the stability domain boundaries is inefficient.
Aiming at the challenge of high order of the new energy station model, most researches adopt a reduced order or equivalent model when analyzing the new energy multi-machine model. Related researches adopt a balance realization theory to discard a non-dominant oscillation mode of a multi-voltage source converter (Voltage Source Converter, VSC for short) grid-connected system, but the non-dominant oscillation mode may cause partial coupling characteristic loss in a field; and when the operation working condition changes, the dominant oscillation mode reserved by the reduced order model is difficult to ensure to have consistent small disturbance characteristics. The related research adopts an equivalent method to equivalent the new energy station model to a single machine or multiple machine model; however, the equivalent method only focuses on the interaction mechanism of the whole new energy station and the power grid, and ignores the coupling characteristic between single machines.
The key to constructing a small perturbation stability domain is to determine its stability domain boundaries. The parameter stability domain is analyzed by related research, but the constructed stability domain changes along with the change of working conditions, so that guidance is difficult to provide in practical application. The related research adopts a point-by-point method to calculate the system stability under different serial complement values, and establishes a stable domain boundary of single parameters related to the serial complement values; however, the point-by-point method has the problem of large calculation amount, and is difficult to apply online. Related researches aim at micro-grid application scenes, active power stability domain boundaries of two VSCs are fitted based on kernel ridge regression, but the fitting method does not consider time-varying characteristics of the power grid. The related research is based on the offline construction of the stable domain boundary of the polymerization impedance and the prediction correction method, and compared with a traversal method, the calculation efficiency is improved; however, the calculation time of the adopted method is still long, and the method is difficult to be suitable for online application of stable domain solving.
Disclosure of Invention
In order to solve the problems, the invention provides a voltage source converter stable domain construction method and a system based on piecewise affine.
According to some embodiments, the first scheme of the invention provides a voltage source converter stability domain construction method based on piecewise affine, which adopts the following technical scheme:
a voltage source converter stable domain construction method based on piecewise affine comprises the following steps:
obtaining an impedance model of the voltage source converter;
constructing a segmented affine impedance model of the voltage source converter based on the segmented affine and the acquired impedance model;
solving the constructed piecewise affine impedance model to finish the construction of the stable domain of the voltage source converter;
in the process of solving the constructed segmented affine impedance model, a double-layer optimization solving model is adopted, an inner layer model in the double-layer optimization solving model is combined with the constructed segmented affine impedance model and a Nyquist criterion to judge the stability of the working point in the small interference stable domain of the voltage source converter, the inner layer model is used as the nonlinear constraint of an outer layer model in the double-layer optimization solving model, so that the solving of the model is completed, and the construction of the stable domain of the voltage source converter is realized.
As a further technical definition, in the process of constructing the piecewise affine impedance model of the voltage source converter, the acquired impedance model of the voltage source converter is converted into a piecewise low-order linear sub-model based on the piecewise affine theory.
As a further technical definition, the piecewise affine comprises constructing a voltage source converter impedance dataset, constructing dataset partitions according to a clustering algorithm, and implementing parameter estimation of an affine sub-model based on a least squares method.
As a further technical definition, the constructed piecewise affine impedance model of the voltage source converter is a dq coordinate system based on the voltage orientation of the grid-connected point of the voltage source converter itself; when a plurality of voltage source converters are connected in a grid, each constructed voltage source converter impedance model is transformed to the same dq coordinate system, and a multi-machine impedance model is obtained.
As a further technical limitation, in the process of judging the stability of the operating point in the small-interference stable domain of the voltage source converter, analyzing whether the return rate matrix meets the generalized nyquist criterion or not, namely, when the root tracks of two characteristic roots of the return rate matrix are not surrounded by (0, 1) on a complex plane, the operating point in the small-interference stable domain of the voltage source converter is stable; otherwise unstable.
As a further technical limitation, in the process of carrying out model solving, an inner layer model in the double-layer optimization solving model is solved by adopting an improved Nyquist stability criterion, and an outer layer model in the double-layer optimization solving model is solved by adopting a complex shape method.
As a further technical definition, the nonlinear constraint of the outer layer model in the double-layer optimization solution model is thatWherein P is VSC Is the active output of the voltage source converter, Q VSC Reactive power output of the voltage source converter; f (P) VSC ,Q VSC ) =0 satisfies the tide equation for the running operating point; p (P) min And P max The upper limit and the lower limit of the active output of the voltage source converter are respectively set; q (Q) min And Q max The reactive power output upper limit and the reactive power output lower limit of the voltage source converter are respectively; v rate Output rated voltage for voltage source converter port, v s The actual output voltage of the voltage source converter port; alpha is the power growth direction.
According to some embodiments, the second scheme of the invention provides a voltage source converter stability domain construction system based on piecewise affine, which adopts the following technical scheme:
a piecewise affine-based voltage source converter stability domain construction system comprising:
an acquisition module configured to acquire an impedance model of the voltage source converter;
a building block configured to build a segmented affine impedance model of the voltage source converter based on the segmented affine and the acquired impedance model;
the solving module is configured to solve the constructed piecewise affine impedance model to complete the construction of the stable domain of the voltage source converter;
In the process of solving the constructed segmented affine impedance model, a double-layer optimization solving model is adopted, an inner layer model in the double-layer optimization solving model is combined with the constructed segmented affine impedance model and a Nyquist criterion to judge the stability of the working point in the small interference stable domain of the voltage source converter, the inner layer model is used as the nonlinear constraint of an outer layer model in the double-layer optimization solving model, so that the solving of the model is completed, and the construction of the stable domain of the voltage source converter is realized.
According to some embodiments, a third aspect of the present invention provides a computer-readable storage medium, which adopts the following technical solutions:
a computer readable storage medium having stored thereon a program which when executed by a processor implements the steps in a method for piecewise affine-based voltage source converter stability domain construction according to the first aspect of the present invention.
According to some embodiments, a fourth aspect of the present invention provides an electronic device, which adopts the following technical solutions:
an electronic device comprising a memory, a processor and a program stored on the memory and executable on the processor, the processor implementing the steps in the piecewise affine-based voltage source converter stability domain construction method according to the first aspect of the present invention when the program is executed.
Compared with the prior art, the invention has the beneficial effects that:
the method is based on a piecewise affine theory and establishes a VSC impedance piecewise affine model; and a method for establishing a data set and a partition is provided for the VSC small disturbance model, so that the searching efficiency of affine coefficients and the accuracy of the affine model are ensured. And establishing a multi-machine VSC segmented affine model, retaining the frequency domain impedance information of the original system, and greatly reducing the model order.
The invention provides a construction method of a boundary of a VSC stable domain, which comprises the steps of constructing a double-layer optimization model for solving boundary points of the VSC stable domain, and solving the optimization model based on an improved generalized Nyquist stability criterion and a complex shape method; and then searching boundary points by changing the solving direction of the double-layer optimization model and performing segmentation fitting, so that the accuracy of the boundary of the stable domain is ensured and the construction efficiency is improved.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments and are incorporated in and constitute a part of this specification, illustrate and explain the embodiments and together with the description serve to explain the embodiments.
Fig. 1 is a diagram of a single VSC grid-connected structure in a first embodiment of the present invention;
FIG. 2 is a schematic illustration of a piecewise affine in accordance with one embodiment of the present invention;
FIG. 3 is a schematic diagram of a segmented affine partition according to a first embodiment of the invention;
fig. 4 is a diagram of a multi-VSC grid-connected structure in a first embodiment of the present invention;
FIG. 5 is a schematic diagram of a VSC small disturbance stability domain boundary according to a first embodiment of the present invention;
FIG. 6 is a schematic diagram of an improved generalized Nyquist stability criterion in accordance with a first embodiment of the present invention;
FIG. 7 is a flow chart of a solution for boundary conditions of a VSC stability domain based on a complex shape method according to a first embodiment of the invention;
FIG. 8 is a schematic diagram of iterative solution of a complex method in accordance with a first embodiment of the present invention;
FIG. 9 is a schematic diagram of a VSC small disturbance stability domain boundary solution in accordance with a first embodiment of the present invention;
FIG. 10 is a flow chart of an online quick construction of a VSC stability domain boundary in accordance with a first embodiment of the present invention;
FIG. 11 is a graph showing the stability domain accuracy contrast of the method and the spread point traversal method according to the first embodiment of the invention at different SCRs;
fig. 12 is a schematic diagram of single VSC stability domain boundary time domain verification at scr=1.7 in the first embodiment of the present invention;
FIG. 13 is a comparison of multiple VSC stability domains under different SCRs in accordance with an embodiment of the present invention
Fig. 14 is a schematic diagram of multi-machine VSC stability domain boundary time domain verification at scr=1.7 in the first embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
Embodiments of the invention and features of the embodiments may be combined with each other without conflict.
Example 1
The embodiment of the invention introduces a voltage source converter stability domain construction method based on piecewise affine.
The embodiment adopts a piecewise affine theory to convert VSC impedance into a linear form, and simultaneously provides a stable domain construction method capable of meeting online application; for complex high-order VSC impedance small disturbance models, the segmentation method of segmented affines and affine sub-model parameter identification are challenging. And, how to further improve the stability domain boundary rapid construction efficiency based on the piecewise affine impedance model is also challenging.
According to the VSC model shown in fig. 1, which mainly comprises a current loop control and a phase-locked loop control of the current transformer, an impedance model is established, which analyzes small disturbance stability. In the dq coordinate system, the two-dimensional matrix of VSC impedance is as follows:
wherein P is VSC And Q VSC Active and reactive power of VSC output, v s Representing the grid tie point voltage. In the frequency domain s=j2pi f is a complex state variable, where f is frequency.
The VSC impedance characteristics are affected by the operating point, and are related to active, reactive and port voltages. In order to construct a VSC segmented affine model more suitable for practical applications, the running operating point state variables are defined as:
x＝[P VSC Q VSC v s ] (2)
as shown in fig. 2, the complex high-order VSC impedance model with respect to the operating points x and s is converted into a piecewise low-order linear submodel based on piecewise affine theory. The piecewise affine specifically comprises three steps: constructing a VSC impedance data set, constructing a data set partition according to a clustering algorithm, and realizing parameter estimation of an affine submodel based on a least square method.
1) Impedance data set construction method
Since the input variables have different units and ranges, normalization processing is performed on all the input variables x. And calculating the corresponding VSC output impedance under different x and s within the operable range, and constructing a sample data set.
The present embodiment proposes to construct the VSC impedance dataset by linearity analysis to avoid the influence of sample set density on the accuracy and computational efficiency of the segmented affine model.
Formula (1) relates to P VSC ，Q VSC ，v s And s have different linearities. With impedance element Z dd For the example of linearity of s, a linear correlation coefficient r is defined as:
where Cov is the covariance calculation symbol and Var is the standard deviation calculation symbol. The molecules of the linear correlation coefficient are Z dd (s) real and imaginary covariance. The denominator of the linear correlation coefficient is Z dd (s) the product of the real and imaginary standard deviations. The linear correlation coefficient is between 0 and 1, the closer it is to 1, the higher the linearity of the two variables.
According to the linearity of the VSC working points x and s with respect to the impedance, scattering is performed when constructing a sample set, and the sample space is preliminarily divided into different data sets.
2) Data clustering and partition space solving
The data set obtained in the step 1) contains a large number of sample points, and a data clustering method is adopted to divide a sample space. A data set space may be divided into disjoint subspaces, each of which may be represented by a low-order linear analytical formula.
In the embodiment, a hierarchical clustering method is adopted to cluster the data of the data set. The main idea is that initially each data is considered as a class, the Euclidean distance is used to calculate the sample class S 1 ，S 2 Is a distance of (3). In Z dd (x, s) for example, the Euclidean distance e between its samples is:
the maximum sample distance between the two classes is taken as the true distance E (S 1 ,S 2 )：
When E (S) 1 ,S 2 ) Beyond the set threshold value psi, aggregation between the two classes is not performed, and the number and the accuracy of clusters are adjusted by adjusting the size of the threshold value psi.
After determining the sample set partition based on the clustering algorithm, solving the interface coefficient of the partition by adopting support vector classification (support vector classification, SVC) [21] . With χ u The partitions of the running points x and s of the piecewise affine model are represented, the subscript u represents the number of the partition, and the expression of the interface can be expressed as:
χ u ＝{F u [x s] T +g u ，，0} (6)
wherein F is u And g u Is an interface coefficient matrix.
As shown in FIG. 3, in Z dd Visual partition indications are given for the examples. When the parameters of the power grid are determined, the port voltage can be determined according to the active and reactive power flow, s is taken to be 5-15Hz, P VSC At 0-25kW, Q VSC Between 0 and 10kVar as a data set. The segmented affine partitioning result is shown in fig. 3, and the hierarchical clustering algorithm divides the sample space into 4 pieces, and the interface coefficient matrix of each subspace is obtained according to SVC.
3) Affine sub-model parameter estimation
Based on the data in the partition of step 2), the sub-model parameter beta is identified by utilizing a parameter estimation method u . After decomposing the dataset according to step 1) and clustering the partitions according to step 2), the sub-partitions are then partitionedThe linearity of the internal data is high, and a first-order linear expression fitting can be adopted. In Z dd For example, its piecewise affine model is expressed as:
wherein beta is u ＝[β u,1 β u,2 β u,3 β u,4 β u,5 ]Coefficient parameter of the u-th affine sub-model, χ u And the U state variable partition space is represented, and U is the total number of partitions in the operation point and the full frequency domain space.
Realizing parameter beta in (7) based on least square method u Is a single-chip microcomputer. For the (u) th χ u The v-th sample point x within the partition u,v Defining an error distance as follows:
where v is the sample point number. By making J u The sum of squares of the distances from each sample point to the fitting equation is minimum, and the optimal affine sub-model parameter beta is obtained u ：
Each partition executes least square fitting, and a segmented affine impedance model of the VSC under the full working condition and the full frequency band can be obtained, which is expressed as follows:
wherein the VSCThe other three terms of the impedance matrix are equally available from (7).
And establishing a piecewise affine impedance model about the operation working points x and s for the VSC, converting the high-order nonlinear model into a partitioned first-order piecewise affine model, and greatly reducing the impedance order of the VSC. In practical application, the port characteristic of the VSC can be obtained according to the load flow operation, and then the partition submodel is searched to obtain a low-order impedance expression.
When the VSCs are connected, each VSC impedance model is built based on a dq coordinate system oriented by the voltage of the self-connected point. Because of the influence of the current collecting circuit, the voltages of the grid connection points are different, and the grid connection points cannot be directly connected to form an impedance network. The multi-machine impedance model is built by transforming each VSC impedance model into a unified dq coordinate system. The multi-machine VSC grid-connected structure is shown in fig. 4, wherein grid nodes are used as reference nodes, and the rest VSC nodes are used as PQ nodes. The operating point x of each VSC is obtained through load flow calculation, and meanwhile, the angle difference theta between the VSC node and the reference node can also be obtained VSC,k 。
According to (10), the impedance model of the kth VSC transformed into the unified dq coordinate system is:
wherein x is VSC,k Is an operating point state variable, T, of the kth VSC defined according to equation (2) dq,k Is defined as follows:
the line impedance and the output impedance of the VSC are adopted for series-parallel connection to obtain the aggregate impedance Z of the multi-VSC field farm Finally, a multi-VSC segmented affine impedance model can be obtained,
wherein x is farm ＝[x VSC,1 ,…,x VSC,k ,…,x VSC,K ] (14)
The impedance characteristics are accurately reflected according to x and s, so that the effectiveness of actual operation is greatly improved.
In a multi-VSC application, the impedance characteristics of each VSC may directly determine the low-order impedance expression based on the port characteristics. The problem that when the working condition changes, the high-order impedance of each VSC needs to be recalculated is avoided. And as the number of VSCs becomes larger, the advantage of the piecewise affine model is more obvious, so that the computational complexity can be greatly reduced.
The key to constructing a stability domain is to quickly determine a stability boundary, which consists of a series of operating points at critical steady state. Therefore, the embodiment provides a double-layer optimization model for quickly solving the boundary points of the stable domain, so that the construction efficiency and accuracy of the boundary of the small-interference stable domain of the VSC system can be improved.
As shown in fig. 5, the VSC small disturbance stability domain is surrounded by a series of discrete operating condition critical points (black dots) on the boundary. And judging the stability of each working condition point according to the generalized Nyquist criterion. VSC grid-connection stability can be determined by analyzing whether the return rate matrix L(s) satisfies the generalized nyquist criterion: on the complex plane, when two characteristic roots lambda of L(s) 1 ，λ 2 When none of the trajectory curves of (1, 0) is enclosed, the system is stable; otherwise, the system is unstable. Wherein the recovery matrix is expressed as:
wherein the equivalent impedance at the grid side is denoted as Z grid 。
In fig. 5 d represents the power limit for safe and stable operation in the power increase direction α. Solving the stability domain boundary problem may translate into solving a critical stable operating point for each power increase direction.
Aiming at the problems, the embodiment provides a double-layer optimization solving model which is divided into an inner layer model and an outer layer model: solving the stability of each working point by the inner layer model based on a generalized Nyquist criterion; and solving the power limit which can stably run under the power increasing direction by the outer layer model. The inner layer model needs to determine the operation condition for solving, and the power increase limit of the outer layer model is limited by the stability margin of the inner layer model.
1) Inner layer optimization model
g RE For when the imaginary part of the characteristic root trace is equal to 0, i.e. Im (lambda) 1,2 (s,P VSC ,Q VSC ) For example, =0), the abscissa of the smallest intersection point on the real axis. When g RE When the total weight of the total weight is greater than-1, the system is stable, g RE And the system is critically stable when being equal to-1. Otherwise, the system is unstable. The decision variable of the inner layer model is P VSC ，Q VSC And s, the optimization target is according to the characteristic root lambda 1 ，λ 2 Solving g by trajectory curve of (2) RE . The inner layer optimization problem thus constructed is:
wherein f (P VSC ,Q VSC ) =0 satisfies the tide equation for the running operating point; p (P) min And P max The upper and lower limits of active force of the VSC; q (Q) min And Q max The reactive output upper and lower limits of the VSC are respectively set; v rate The rated voltage is output to the VSC port, and the VSC is required to meet the condition that the port voltage is not out of limit during operation.
According to the optimization target g RE Defining stability margin M of a system G ：
M G (s,P VSC ,Q VSC )＝-20log(|g RE (s,P VSC ,Q VSC )|) (17)
2) Outer layer optimization model
The optimization goal of the stability domain boundary outer layer optimization model is the maximum power limit d along a certain power increase direction, and the decision variable is P VSC And Q VSC . The outer layer optimization problem thus constructed is:
wherein M is G Is coming fromStability margin constraints solved from the inner layer model. According to equation (18), after the power growth direction is determined, the problem of solving the boundary point of the critical stable domain can be converted into the maximum active and reactive output under the condition that the solution meets the constraint condition.
In solving the double-layer optimization problem, the inner layer and the outer layer are mutually limited, which greatly increases the calculation time. The section proposes to construct an improved generalized Nyquist criterion suitable for double-layer optimization model calculation, which mainly solves the problem of long solving time of an inner-layer model.
As shown in fig. 6, an improved generalized nyquist stabilization criterion is proposed, delineating forbidden viable domains. And a rectangular area with a real axis less than xi and a height epsilon taking the real axis as a center on the complex plane is shown as the following formula:
compared with the Middlebrook criterion and the GMPM criterion, the criterion method provided by the embodiment has lower conservation in stability judgment and is more suitable for practical application. When ε=0, the forbidden feasible region becomes the forbidden region of generalized Nyquist. The improved nyquist criterion is shown in formula (20):
when the nyquist curve passes through the red region, it is noted as-1, indicating instability. Otherwise, it is denoted as 1, indicating stability.
Latin hypercube sampling is carried out on s, and g is avoided by judging whether sampling points are located in forbidden domains or not RE Is a solution to the problem. And the symbol operation is converted into the numerical value calculation by utilizing a sampling point mode, so that the calculation efficiency can be remarkably improved.
Introducing an improved generalized Nyquist criterion according to the double-layer optimization model and the inner-layer optimization model, and introducing M label (P VSC ,Q VSC ) Substituting the constraints into the outer layer optimization model. Thereby changing the inner layer optimizing model into the outer layer optimizing modelNonlinear constraint of the form, formula (18) becomes the following formula:
the complex method is a nonlinear global optimization algorithm and does not need an explicit analytical expression of an optimization target or constraint condition. In solving the problem of equation (21), the complex method may better incorporate equation (20) into the constraint. The algorithm flow chart shown in fig. 7 mainly takes n points, and finds the worst solution and the best solution of the target result during iteration. The worst solution is then mapped to the center of the remaining n-1 points. If the mapped target result does not meet the limit of the optimization problem or the target result is worse, the mapping distance is reduced. When the errors of the n points are all iteratively converged to be smaller than the set threshold value, the iteration is stopped. n is typically 10 times the number of variables.
P with a constant power growth direction in the application of the present embodiment VSC And Q VSC Is fixed, thus taking the variable P in the complex method VSC And n=10. The principle of iterative solution of the complex method shown in FIG. 8, P w Representing the worst solution in this iteration, P b Represents the optimal solution, P c Representing the centroid, calculated according to the following formula:
P map is P w According to P c The mapped points are calculated according to the following equation:
P map ＝P c +γ(P c -P w ) (23)
where γ represents a mapping coefficient, and is set to 1.3 in this embodiment.
For P in 10 points in each iteration w And mapping, wherein when the 10 points are subjected to iterative mapping and all meet the set threshold range, iteration is stopped, and an optimal solution is obtained.
As shown in FIG. 9, in the construction of VWhen SC stabilizes a domain boundary, a series of discrete points on the boundary are required, each of which can be found by the complex method. The search is performed by a step size of delta alpha over a range of angles alpha (-90 deg., 90 deg.). Where Δα is searched in initially large angular increments. As indicated by blue arrows, each two adjacent discrete points are calculated at alpha i Boundary point (P) in +Δα/2 power increase direction check ,Q check ) As an error detection point. The linearization analytical formula for obtaining the boundary according to the ith and the (i+1) th points on the boundary is as follows:
calculation (P) check ,Q check ) Distance d to line segment shown in (23) error The method comprises the following steps:
when 0 is<d error <d limit When the boundary line segment is considered to meet the set boundary precision; when d error >d limit At this time, the angle increment Δα=Δα/2 is adjusted, and then d is calculated error Until it meets the boundary error accuracy.
Error of the j-th line segment as shown in fig. 9. When d error <At 0, the boundary of the stable region formed at this time has a small unstable region inside. At this time, an improved generalized Nyquist stability criterion is utilized for the inner layer optimization model. By increasing the rectangular forbidden domain shown in FIG. 6, i.e., increasing the values of ε and ζ, the stable domain is made more conservative, up to 0 <d error <d limit The occurrence of unstable small areas is avoided.
As shown in fig. 10, specific steps of an online rapid construction method for a stability domain boundary of a VSC piecewise affine impedance model are given: first, data is initialized, and a starting angle and an increment thereof are set. And then solving boundary points based on a complex shape method, and performing error detection between every two points. And correcting the points which are not satisfied by the errors. And finally, obtaining an analytic expression by segment fitting to obtain a complete boundary. By reasonably changing the growth direction of the search power, the stable domain can be ensured to have higher calculation efficiency and more accurate boundary, and the online construction is completed.
Calculation case analysis
The single-machine VSC simulation model shown in the figure 1 is built, and compared with the existing method from the two angles of accuracy and calculation efficiency of single-machine VSC stable domain construction respectively; firstly, comparing a point-by-point traversal method with a double-layer optimization method proposed by the embodiment, and comparing the boundary differences of stable domains under different short circuit ratios (Short circuit ratio, SCR); and when scr=1.7, stability domain boundary validity verification is performed. Secondly, comparing the calculation time of different methods, verifying the stability domain construction method based on the VSC segmented affine model has high calculation efficiency.
The method and the point-by-point traversal method provided by the embodiment are adopted to establish the stable domains of the active power and the reactive power of the VSC. As shown in fig. 11, the boundary errors are compared in three cases of scr=1.4, scr=1.7, and scr=2.0, respectively. As can be seen, the point-by-point traversal method and the method proposed in this example yields consistent boundaries with minimal errors. Therefore, the method provided by the embodiment can accurately search the stability domain boundary. By comparing the stability domain boundaries under different SCRs, the smaller the grid SCR, the smaller the stability domain the system can operate. For a given example, the change rule of active power and reactive power is observed, which shows that the VSC under the weak current network can appear under the unstable condition along with the increase of active power, and the stability of the system can be improved by properly increasing reactive power.
Three operating points, operating 1, are shown in FIG. 11: p (P) VSC ＝22kW，Q VSC =0 kVar; working condition 2: p (P) VSC ＝23kW，Q VSC =0 kVar; working condition 3: p (P) VSC ＝23kW，Q VSC =2kvar. As shown in fig. 12, the stability under these three conditions was compared in the simulation. Before t is less than 5s, the system is operated under the working condition 1 and is in stable operation. The system increases the active power output at 5 s. At 6.5s the system is at regime 2 and the system begins to oscillate at 9Hz, with a subsequent gradual increase in oscillation amplitude. Reactive output increase at 7.5sUp to 2kVar, the system is at regime 3. The oscillation amplitude then begins to decrease and the system gradually resumes steady state operation. The accuracy of the boundary of FIG. 11 is verified by the time domain simulation result, and in practical application, the operation condition can be adjusted according to the stability domain, so that the stable operation of the system is ensured.
Aiming at four methods of a point-by-point traversal method, a prediction correction method, a double-layer optimization method of a VSC full-order model and a double-layer optimization method of a VSC segmented affine model, the search efficiency of a comparison boundary is ensured under the same search precision. The calculated time comparisons for the four methods are shown in Table 1:
TABLE 1 grid-connected stability Domain boundary calculation time comparison
The boundary search method has an advantage in the calculation speed of each operating point over the point-by-point traversal method and the prediction correction method. And in the number of working condition points to be calculated, the traversal method is the most, the prediction correction is less, and the embodiment has the advantage in calculation speed by the least calculation of the optimization method. The method 4 greatly improves the speed of solving the impedance during calculation by adopting the piecewise affine model, improves the calculation efficiency by more than 2 times compared with the third method, and proves the effectiveness of adopting the piecewise affine model. The calculation efficiency (inverse proportion of calculation time) of the comparison traversal method and the prediction correction method in the method proposed by the embodiment is 54 and 6.45, and the calculation time meets the requirement of on-line operation.
The method of the embodiment supports the online construction of the stable domains of a plurality of VSCs. And building a four-machine VSC simulation model according to the VSC parallel structure shown in FIG. 4. Stability between VSCs is analyzed under a weak current network, and for convenience and intuitionistic presentation, the stability domain of active power between the branch 1 and the branch 2 is focused in verification of the embodiment. Setting the reactive power output of 4 VSCs to 0, fixing the active power output of the third VSC to 23kW, and the active power output of the fourth VSC to 20kW. As shown in fig. 13, P at scr=1.6, scr=1.7, and scr=1.8 was compared VSC1 And P VSC2 Is a stable domain of operation of (a). The smaller the SCR, the smaller the operational stability domain. Three working conditions are set, namely, working condition 1: p (P) VSC1 ＝14kW，P VSC2 =20 kW; working condition 2: p (P) VSC1 ＝16kW，P VSC2 =20 kW; working condition 3: p (P) VSC1 ＝16kW，P VSC2 ＝17kW。
As shown in FIG. 14, the accuracy of the stability domain boundary was verified by simulation. The system is in a steady state at condition 1, the active power of the VSC connected to branch 1 begins to increase at 5s, condition 2 is reached at 7.5s, and the system begins to generate an oscillation frequency of 8 Hz. And at 8s, the VSC connected through the branch circuit 2 reduces the power output to the working condition 3, and the system gradually recovers to be stable. The time domain simulation result verifies the effectiveness and accuracy of the method in the multi-machine VSC stability domain structure. In actual operation, a stable domain among the multi-machine interconnected VSCs can be constructed, and the output of each VSC is distributed through field control, so that the system is in a stable state. If oscillation occurs, the output of each VSC can be reasonably regulated and controlled to enable the system to restrain the oscillation.
As shown in table 2, the computational efficiency of the four-machine VSC stability domain boundary configuration was compared with method 3 and method 4. The efficiency ratio is calculated to be 5.98 by a double-layer optimization method based on the segmented affine impedance model and the impedance full-order model. The necessity of a segmented affine model to be applied to the stable domain boundary construction is demonstrated. The application of the piecewise affine impedance model can increase the computational efficiency by a factor of 2 compared to a single VSC stability domain configuration, indicating that the piecewise affine impedance model has more significant advantages in a larger scale system.
Table 2 4 VSC grid-connected stability area boundary calculation time comparison
The embodiment establishes a VSC impedance piecewise affine model based on piecewise affine theory; providing a method for establishing a data set and a partition for the VSC small disturbance model, and ensuring the searching efficiency of affine coefficients and the accuracy of the affine model; and establishing a multi-machine VSC segmented affine model, retaining the frequency domain impedance information of the original system, and greatly reducing the model order.
The embodiment provides a construction method of a boundary of a VSC stability domain, a double-layer optimization model for solving boundary points of the VSC stability domain is constructed, and the optimization model is solved based on an improved generalized Nyquist stability criterion and a complex method; and then searching boundary points by changing the solving direction of the double-layer optimization model and performing segmentation fitting, so that the accuracy of the boundary of the stable domain is ensured and the construction efficiency is improved.
The embodiment verifies the accuracy of the piecewise affine model by comparing the errors with the impedance full-order model. And the accuracy and the effectiveness of the method in the aspect of constructing the stable domain are verified through single VSC and multi-VSC simulation. Compared with the existing method, the method in the embodiment can remarkably improve the calculation efficiency.
Example two
The second embodiment of the invention introduces a voltage source converter stability domain construction system based on piecewise affine.
A piecewise affine-based voltage source converter stability domain construction system comprising:
an acquisition module configured to acquire an impedance model of the voltage source converter;
a building block configured to build a segmented affine impedance model of the voltage source converter based on the segmented affine and the acquired impedance model;
the solving module is configured to solve the constructed piecewise affine impedance model to complete the construction of the stable domain of the voltage source converter;
in the process of solving the constructed segmented affine impedance model, a double-layer optimization solving model is adopted, an inner layer model in the double-layer optimization solving model is combined with the constructed segmented affine impedance model and a Nyquist criterion to judge the stability of the working point in the small interference stable domain of the voltage source converter, the inner layer model is used as the nonlinear constraint of an outer layer model in the double-layer optimization solving model, so that the solving of the model is completed, and the construction of the stable domain of the voltage source converter is realized.
The detailed steps are the same as those of the voltage source converter stability domain construction method based on piecewise affine provided in the first embodiment, and are not described herein again.
Example III
The third embodiment of the invention provides a computer readable storage medium.
A computer readable storage medium having stored thereon a program which when executed by a processor performs the steps in a method for piecewise affine-based voltage source converter stability domain construction according to an embodiment of the present invention.
The detailed steps are the same as those of the voltage source converter stability domain construction method based on piecewise affine provided in the first embodiment, and are not described herein again.
Example IV
The fourth embodiment of the invention provides electronic equipment.
An electronic device comprising a memory, a processor and a program stored on the memory and executable on the processor, the processor implementing the steps in a method for constructing a voltage source converter stability domain based on piecewise affine according to an embodiment of the invention when the program is executed.
The detailed steps are the same as those of the voltage source converter stability domain construction method based on piecewise affine provided in the first embodiment, and are not described herein again.
The above description is only a preferred embodiment of the present embodiment, and is not intended to limit the present embodiment, and various modifications and variations can be made to the present embodiment by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present embodiment should be included in the protection scope of the present embodiment.
Claims (5)
1. The utility model provides a voltage source converter stable domain construction method based on piecewise affine which is characterized by comprising the following steps:
obtaining an impedance model of the voltage source converter;
constructing a segmented affine impedance model of the voltage source converter based on the segmented affine and the acquired impedance model;
solving the constructed piecewise affine impedance model to finish the construction of the stable domain of the voltage source converter;
in the process of solving the constructed segmented affine impedance model, a double-layer optimization solving model is adopted, an inner layer model in the double-layer optimization solving model is combined with the constructed segmented affine impedance model and a Nyquist criterion to judge the stability of the working point in the small interference stable domain of the voltage source converter, the inner layer model is used as the nonlinear constraint of an outer layer model in the double-layer optimization solving model, so that the solving of the model is completed, and the construction of the stable domain of the voltage source converter is realized;
constructing a segmented affine impedance model of the voltage source converter based on the segmented affine and the acquired impedance model; the method comprises the following steps:
the voltage source converter model mainly comprises converter current loop control and phase-locked loop control, and an impedance model for analyzing small disturbance stability is established; in the dq coordinate system, the two-dimensional matrix of VSC impedance is as follows:
Wherein P is VSC And Q VSC Active and reactive power of VSC output, v s Representing grid-connected point voltage; s=j2pi f is a complex state variable in the frequency domain, where f is frequency;
the impedance characteristic of the voltage source converter is affected by an operation working point and is related to the active power, the reactive power and the port voltage; in order to construct a voltage source converter piecewise affine model more suitable for practical application, the operating point state variables are defined as:
x＝[P VSC Q VSC v s ] (2)
based on piecewise affine theory, converting a complex high-order voltage source converter impedance model about operation working points x and s into a piecewise low-order linear sub-model; the piecewise affine specifically comprises three steps: constructing a voltage source converter impedance data set, constructing a data set partition according to a clustering algorithm, and realizing parameter estimation of an affine sub-model based on a least square method;
step one: impedance data set construction method
Because the input variables have different units and different ranges, normalizing all the input variables x; calculating output impedance of the voltage source converter corresponding to different x and s in an operable range, and constructing a sample data set;
step two: data clustering and partition space solving
The data set obtained in the first step contains a large number of sample points, and a data clustering method is adopted to divide a sample space; a data set space may be divided into a plurality of disjoint subspaces, each subspace may be represented by a low-order linear analytical formula;
Step three: affine sub-model parameter estimation
Based on the data in the second partition, the sub-model parameter beta is identified by utilizing a parameter estimation method u The method comprises the steps of carrying out a first treatment on the surface of the After decomposing the data set according to the first step and aggregating the class partition according to the second step, the linearity of the data in the sub-partition is higher at the moment, and first-order linear expression fitting can be adopted; z is Z dd The piecewise affine model is expressed as:
wherein beta is u ＝[β u,1 β u,2 β u,3 β u,4 β u,5 ]Coefficient parameter of the u-th affine sub-model, χ u The U state variable partition space is represented, and U is the total number of partitions in the operating point and the full frequency domain space;
each partition executes least square fitting, and a segmented affine impedance model of the voltage source converter under the full working condition and the full frequency band can be obtained, which is expressed as follows:
wherein the voltage source converterObtained by (7);
according to (10), the impedance model of the kth voltage source converter transformed into the unified dq coordinate system is:
wherein x is VSC,k Is the operating point state variable, T, of the kth voltage source converter defined according to formula (2) dq,k Is defined as follows:
wherein θ VSC,k The angle difference between the voltage source converter node and the reference node is;
the line impedance and the output impedance of the voltage source converter are adopted for series-parallel connection to obtain the aggregate impedance Z of the multi-voltage source converter field farm Finally obtaining a segmented affine impedance model of the multi-voltage source converter,
wherein x is farm ＝[x VSC,1 ,…,x VSC,k ,…,x VSC,K ] (14)
Solving the constructed piecewise affine impedance model to finish the construction of the stable domain of the voltage source converter; the method comprises the following steps:
the key to constructing a stability domain is to quickly determine a stability boundary, which is composed of a series of operating points in a critical steady state; adopting a double-layer optimization model for rapidly solving boundary points of a stable domain, and improving the construction efficiency and accuracy of a small-interference stable domain boundary of a voltage source converter system;
the small interference stable domain of the voltage source converter is formed by surrounding a series of discrete working condition critical points on the boundary; the stability of each working point is judged according to a generalized Nyquist criterion; grid-connected stability of the voltage source converter can be achieved through dividingWhether the resolution matrix L(s) satisfies the generalized nyquist criterion: on the complex plane, when two characteristic roots lambda of L(s) 1 ，λ 2 When none of the trajectory curves of (1, 0) is enclosed, the system is stable; otherwise, the system is unstable; wherein the recovery matrix is expressed as:
wherein the equivalent impedance at the grid side is denoted as Z grid ；
d represents the power limit of safe and stable operation in the power increasing direction alpha; solving the stability domain boundary problem can be converted into solving critical stability working points under each power increasing direction;
The method adopts a double-layer optimization solving model which is divided into an inner layer model and an outer layer model: solving the stability of each working point by the inner layer model based on a generalized Nyquist criterion; the outer layer model solves the power limit which can stably run under the power increasing direction; the inner layer model needs to determine the operation condition for solving, and the power increase limit of the outer layer model is limited by the stability margin of the inner layer model;
1) Inner layer optimization model
g RE For when the imaginary part of the characteristic root trace is equal to 0, i.e. Im (lambda) 1,2 (s,P VSC ,Q VSC ) A abscissa of the smallest intersection point on the calculated real axis) =0; when g RE When the total weight of the total weight is greater than-1, the system is stable, g RE When the system is equal to-1, the system is critically stable; otherwise, the system is unstable; the decision variable of the inner layer model is P VSC ，Q VSC And s, the optimization target is according to the characteristic root lambda 1 ，λ 2 Solving g by trajectory curve of (2) RE The method comprises the steps of carrying out a first treatment on the surface of the The inner layer optimization problem thus constructed is:
wherein f (P VSC ,Q VSC ) =0 satisfies tide for running operating pointAn equation; p (P) min And P max The upper limit and the lower limit of the active output of the voltage source converter are set; q (Q) min And Q max The reactive power output upper limit and the reactive power output lower limit of the voltage source converter are respectively; v rate Outputting rated voltage for a port of the voltage source converter, wherein the voltage source converter is required to meet the condition that the port voltage is not out of limit when in operation;
according to the optimization target g RE Defining stability margin M of a system G ：
M G (s,P VSC ,Q VSC )＝-20log(|g RE (s,P VSC ,Q VSC )|) (17)
2) Outer layer optimization model
The optimization goal of the stability domain boundary outer layer optimization model is the maximum power limit d along a certain power increase direction, and the decision variable is P VSC And Q VSC The method comprises the steps of carrying out a first treatment on the surface of the The outer layer optimization problem thus constructed is:
wherein M is G Is a stability margin constraint from the solution of the inner layer model; alpha is the power increasing direction; according to the formula (18), after the power growth direction is determined, the problem of solving the boundary point of the critical stable domain can be converted into the maximum active and reactive output under the condition that the solution meets the constraint condition;
providing an improved generalized Nyquist stability criterion, and defining a forbidden feasible region; and a rectangular area with a real axis less than xi and a height epsilon taking the real axis as a center on the complex plane is shown as the following formula:
when ε=0, the forbidden feasible region becomes the forbidden region of generalized Nyquist; the improved nyquist criterion is shown in formula (20):
when the nyquist curve passes through the red region, it is noted as-1, indicating instability; otherwise, it is marked as 1, indicating stability;
latin hypercube sampling is carried out on s, and g is avoided by judging whether sampling points are located in forbidden domains or not RE Is a solution process of (2);
introducing an improved generalized Nyquist criterion according to the double-layer optimization model and the inner-layer optimization model, and introducing M label (P VSC ,Q VSC ) Substituting the constraints into the outer layer optimization model; thereby changing the inner layer optimization model to a nonlinear constraint of the outer layer optimization model, and the equation (18) to the following equation:
wherein P is VSC Is the active output of the voltage source converter, Q VSC Reactive power output of the voltage source converter; f (P) VSC ,Q VSC ) =0 satisfies the tide equation for the running operating point; p (P) min And P max The upper limit and the lower limit of the active output of the voltage source converter are respectively set; q (Q) min And Q max The reactive power output upper limit and the reactive power output lower limit of the voltage source converter are respectively; v rate Output rated voltage for voltage source converter port, v s The actual output voltage of the voltage source converter port; alpha is the power increasing direction;
the complex method is a nonlinear global optimization algorithm, and does not need an explicit analysis expression of an optimization target or constraint conditions; in solving the problem of equation (21), the complex method better adds equation (20) to the constraint; taking n points, and finding out the worst solution and the optimal solution of the target result during iteration; mapping the worst solution to the centers of the remaining n-1 points; if the target result after mapping does not meet the limit of the optimization problem or the target result is worse, the mapping distance is reduced; when the errors of the n points are all converged to be smaller than the set threshold value, stopping iteration;
When the direction of the power increase is fixed,P VSC and Q VSC Is fixed, P w Representing the worst solution in this iteration, P b Represents the optimal solution, P c Representing the centroid, calculated according to the following formula:
P map is P w According to P c The mapped points are calculated according to the following equation:
P map ＝P c +γ(P c -P w ) (23)
wherein γ represents a mapping coefficient;
for P in n points in each iteration w Mapping is carried out, and when n points are all satisfied within a set threshold range through iterative mapping, iteration is stopped, and an optimal solution is obtained;
when a stable domain boundary of the voltage source converter is constructed, a series of discrete points on the boundary are needed, and each point can be obtained through a complex shape method; searching according to the step length of delta alpha within the range of (-90 degrees, 90 degrees) through the angle alpha; wherein Δα is searched at an initial larger angular increment; every two adjacent discrete points, calculate at alpha i Boundary point (P) in +Δα/2 power increase direction check ,Q check ) As an error detection point; the linearization analytical formula for obtaining the boundary according to the ith and the (i+1) th points on the boundary is as follows:
calculation (P) check ,Q check ) Distance d to line segment shown in (23) error The method comprises the following steps:
when 0 is<d error <d limit When the ith boundary is consideredThe line segment meets the set boundary precision; when d error >d limit At this time, the angle increment Δα=Δα/2 is adjusted, and then d is calculated error Until it meets the boundary error accuracy;
Error of the j-th line segment: when d error <0, the stable domain boundary formed at this time has an unstable small region inside; in the inner layer optimization model, an improved generalized Nyquist stabilization criterion is utilized; by increasing the rectangular forbidden domain, i.e. increasing the values of ε and ζ, the stable domain is made more conservative, up to 0<d error <d limit The occurrence of unstable small areas is avoided;
the method for quickly constructing the stable domain boundary of the sectional affine impedance model of the voltage source converter on line comprises the following specific steps: firstly, initializing data, and setting an initial angle and an increment thereof; then solving boundary points based on a complex shape method, and performing error detection between every two points; correcting points which are not satisfied by the error; finally, obtaining an analytic type boundary by segment fitting; by reasonably changing the growth direction of the search power, the stable domain can be ensured to have higher calculation efficiency and more accurate boundary, and the online construction is completed.
2. The method for constructing the stable domain of the voltage source converter based on the piecewise affine as claimed in claim 1, wherein the piecewise affine impedance model of the constructed voltage source converter is a dq coordinate system based on the voltage orientation of the voltage source converter itself in the grid-connected point; when a plurality of voltage source converters are connected in a grid, each constructed voltage source converter impedance model is transformed to the same dq coordinate system, and a multi-machine impedance model is obtained.
3. A voltage source converter stable domain construction system based on piecewise affine, based on a voltage source converter stable domain construction method based on piecewise affine according to any of claims 1-2, comprising:
an acquisition module configured to acquire an impedance model of the voltage source converter;
a building block configured to build a segmented affine impedance model of the voltage source converter based on the segmented affine and the acquired impedance model;
the solving module is configured to solve the constructed piecewise affine impedance model to complete the construction of the stable domain of the voltage source converter;
in the process of solving the constructed segmented affine impedance model, a double-layer optimization solving model is adopted, an inner layer model in the double-layer optimization solving model is combined with the constructed segmented affine impedance model and a Nyquist criterion to judge the stability of the working point in the small interference stable domain of the voltage source converter, the inner layer model is used as the nonlinear constraint of an outer layer model in the double-layer optimization solving model, so that the solving of the model is completed, and the construction of the stable domain of the voltage source converter is realized.
4. A computer readable storage medium, on which a computer program is stored, characterized in that the program, when being executed by a processor, implements the steps of the piecewise affine based voltage source converter stability domain construction method of any one of claims 1-2.
5. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the piecewise affine-based voltage source converter stability domain construction method of any one of claims 1-2 when the program is executed.
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