CN112821392B - Static voltage stability boundary calculation method based on all-pure embedding method - Google Patents
Static voltage stability boundary calculation method based on all-pure embedding method Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
Abstract
The invention discloses a static voltage stability boundary calculation method based on an all-pure embedding method, which belongs to the field of power system analysis, and comprises the steps of solving a power flow balance equation of a power system by using the all-pure embedding method containing physical mapping factors so as to obtain an analytic expression in a node voltage power series form; and then, deriving an analytical expression of the static voltage stability boundary based on the Cauchy-Adama theorem, thereby calculating the static voltage stability boundary. The method can rapidly and accurately calculate the static voltage stability boundary in an analytic form by applying a pure embedding method containing physical mapping factors and combining the Cauchy-Adama theorem.
Description
Technical Field
The invention belongs to the field of power system analysis, relates to a method for calculating a static voltage stability boundary of a power system, and particularly relates to a method for calculating a static voltage stability boundary based on an all-pure embedding method.
Background
How to quickly and accurately calculate the static voltage stability boundary of the power system is of great significance for evaluating the voltage stability of the power system.
The traditional continuous power flow method adopts an iterative prediction-correction strategy to solve the static voltage stability boundary, but the method generates huge calculation burden when facing a large-scale power system. Therefore, the scholars propose some newer methods, such as the tangent surface method, the track method, etc., but the methods only use the information of a limited point on the static voltage stability boundary, and the accuracy is difficult to guarantee. In addition, the parametric polynomial method based on the Carler's method can globally approximate the quiescent voltage stability boundary. Generally speaking, the traditional iterative power flow solving algorithms such as newton-raphson method and the like are adopted in all the methods for solving the power flow equation of the power system, and the traditional iterative power flow solving algorithms such as newton-raphson method and the like have divergence problems or generate non-operational solutions to a certain extent, which affects the reliability of the methods. As a non-iterative power flow solving algorithm, the all-pure embedding method can ensure that an operable voltage solution can be obtained when the embedding form is proper, and scholars often combine the all-pure embedding method and the Pade approximate analytic extension technology to solve the static voltage stability boundary, but often take time when facing a large-scale power system. In general, it is difficult to solve the quiescent voltage stability boundary of the power system quickly and accurately with the prior art method.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a static voltage stability boundary calculation method based on a pure embedding method, which can quickly and accurately obtain the static voltage stability boundary of the power system.
In order to achieve the above object, the present invention provides a static voltage stability boundary calculation method based on an all-pure embedding method, including:
a static voltage stability boundary calculation method based on an all-pure embedding method is characterized by comprising the following steps:
s1: solving a power flow balance equation of the power system by using a pure embedding method containing physical mapping factors to obtain an analytic expression in a node voltage power series form;
s2: deriving an analytical expression of the static voltage stable boundary based on the Cauchy-Adama theorem, namely deriving an analytical expression of the static voltage stable boundary of the power system by using the Cauchy-Adama theorem to process a power series expression of the node voltage;
s3: calculating a voltage stability boundary according to an analytical expression of the static voltage stability boundary of the power system, specifically comprising:
s3.1: collecting power generation, load and network data of a power system;
s3.2: substituting the power generation, load and network data of the power system into the formula one in the step S1 to obtain the power series expression of the node voltage
S3.3: power series expression based on node voltage
Analytical expression based on static voltage stability boundary
Calculating S therein r Namely the static voltage stability boundary of the power system.
In the above method, step S1 includes:
s1.1: embedding a physical mapping factor in a power flow balance equation of the power system;
s1.2: solving a power flow balance equation of the electric power system containing the physical mapping factor by using a pure embedding method;
s1.3: and obtaining an analytic expression of the node voltage power series form.
In the above method, the equation is balanced in the original power flow
Embedding an all-pure physical mapping factor s to obtain a power flow balance equation containing the all-pure physical mapping factor s
Where s is an all-pure physical mapping factor that can be used to adjust the operating state of the power system, Y ik Is an element of the ith row and kth column in the nodal admittance matrix, Y ik * Represents Y ik Conjugation of (B) to (C), P i And S i Active and complex power injection, V, representing node i i Is the voltage of node i, V i * Represents V i Conjugation of (2) V k Voltage of a node k adjacent to the node i, V k * Represents V k Conjugation of (2) V sw In order to balance the voltage at the node,
representing a specific magnitude of the voltage at the PV (generator) node i, N being the total number of nodes of the power system, Q i Representing the reactive power injection quantity, V, of node i i (s) and Qi(s) are all pure functions of voltage and reactive power at node i, respectively, in the form of a power series, i.e.
Wherein, V i [n]And Q i [n]The nth order coefficients of the node i voltage power series and the reactive power series are respectively.
In the method, the coefficients of the same order s at two sides of the power flow balance equation containing the all-pure physical mapping factor s are equal in a one-to-one correspondence manner, and the current node voltage power series can be establishedRecursion of coefficients of order (unknown quantity) and of preceding order (known quantity), i.e. V i [n]＝f(V i [0],…,V i [n-1]) N is not less than 1, wherein, V i [n]Coefficient of the nth order, V, of the voltage power series of the node i i [0],…,V i [n-1]The function f represents the recursion relationship between the coefficients of the node voltage power series from 0 th order to (n-1) th order of the node i voltage power series, wherein the current order coefficient is an unknown quantity and the previous order coefficient is a known quantity.
In the method, the 0 th order coefficient V of the voltage power series of the node i can be obtained by substituting s-0 into a power flow balance equation containing a fully pure physical mapping factor s i [0]Then, all coefficients V of the node i voltage power series can be obtained through the recursion relation f between the node voltage power series coefficients i [n]N is more than or equal to 1, thereby obtaining the analytical expression of the power series form of the voltage of the node i
In the above method, step S2, since it is inefficient to calculate the tvs boundary directly according to the cauchy-adama theorem, an analytic relationship between the tvs boundary and the ratio of the coefficients before and after the node voltage power series, that is, the analytic relationship between the tvs boundary and the ratio of the node voltage power series, is derived
Wherein, V i [n]And V i [n+1]Coefficient of the nth and (n +1) th order of the node i voltage power series, S r Is the power system static voltage stability boundary.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects: 1. solving a power flow equation by adopting an all-pure embedding method containing physical mapping factors to obtain an analytic expression of the node voltage in an all-pure power series form; 2. according to the analytical relationship between the static voltage stable boundary and the number of terms of the node voltage power series, which is derived according to the Cauchy-Adam theorem, the static voltage stable boundary can be rapidly and accurately calculated.
Drawings
Fig. 1 is a schematic flowchart of a static voltage stability boundary calculation method based on an all-pure embedding method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram showing an electrical power system having m PQ (load) nodes, p PV (generator) nodes and 1 balancing node according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a network structure of an IEEE 14 node standard power system according to an embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating a calculation result of a static voltage stability boundary of an IEEE 14 node standard 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 is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention aims to solve the technical problem that the stable boundary of the static voltage is difficult to calculate quickly and accurately in the existing method: the method comprises the steps of embedding a physical mapping factor in a power flow equation of the power system, obtaining an analytic expression of a node voltage in a pure power series form, and then deducing an analytic relation between a static voltage stable boundary and a ratio example of coefficients of front and rear terms of the node voltage power series according to the Cauchy-Adam theorem, so that the static voltage stable boundary is calculated quickly and accurately.
Fig. 1 is a schematic flow chart of a static voltage stability boundary calculation method based on an all-pure embedding method according to an embodiment of the present invention, including the following steps:
s1: solving a power flow balance equation of the power system by using a pure embedding method containing physical mapping factors to obtain an analytic expression in a node voltage power series form;
in the embodiment of the present invention, step S1 may be implemented as follows:
fig. 2 shows a power system with m load PQ nodes, p generator PV nodes and 1 balancing node, and the load flow equation is:
wherein, Y ik Is an element of the ith row and kth column in the nodal admittance matrix, P i And S i Active and complex power injection, V, representing node i i Is the voltage of node i, V i * Represents V i Conjugation of (2) V k Voltage of a node k adjacent to the node i, V k * Represents V k Conjugation of (2) V sw In order to balance the voltage at the node,
representing a specific magnitude of the PV (generator) node i voltage, N being the total number of nodes of the power system.
Then, embedding a fully-pure physical mapping factor s in the formula (1) to obtain a power flow balance equation containing the fully-pure physical mapping factor s:
where s is an all-pure physical mapping factor that can be used to adjust the operating state of the power system, Y ik Is an element of the ith row and kth column in the nodal admittance matrix, Y ik * Represents Y ik Conjugation of (B) to (C), P i Representing the active power injection, V, of node i i Is the voltage of node i, V i * Represents V i Conjugation of (b), V k Voltage of a node k adjacent to the node i, V k * Represents V k Conjugation of (2) V sw In order to balance the voltage at the node,
representing a specific magnitude of the voltage at the PV (generator) node i, N beingTotal number of nodes, Q, of an electric power system i Representing the reactive power injection quantity, V, of node i i (s) and Q i (s) all-pure functions of voltage and reactive power at node i, respectively, in the form of a power series, i.e.
Wherein, V i [n]And Q i [n]The nth order coefficients of the node i voltage power series and the reactive power series are respectively.
Then, corresponding and equaling the coefficients of the same order s at two sides of the power flow balance equation containing the all-pure physical mapping factor s, and establishing the recursion relation between the current order coefficient (unknown quantity) and the previous order coefficient (known quantity) of the node voltage power series:
V i [n]＝f(V i [0],…,V i [n-1]),n≥1 (3)
wherein, V i [n]Coefficient of the nth order, V, of the voltage power series of the node i i [0],…,V i [n-1]The function f represents the recursion relationship between the coefficients of the node voltage power series from 0 th order to (n-1) th order of the coefficients of the node voltage power series. Then, if the 0 th order coefficient of the node voltage power series can be obtained, all the coefficients of the node voltage power series can be obtained by the equation (3).
Therefore, the 0 th order coefficient V of the node voltage power series is solved by substituting 0 into a power flow balance equation containing the all-pure physical mapping factor s, namely the formula (2) i [0]Then, all the coefficients V of the node voltage power series can be obtained through the recursion relationship f between the coefficients of the node voltage power series, namely the formula (3) i [n]And n is more than or equal to 1, so that an analytic expression of the node voltage in a power series form is obtained:
in step S1, an analytic expression in the form of a power series of the node voltages of the power system is obtained. S2: deducing an analytical expression of the static voltage stability boundary based on the Cauchy-Adama theorem;
in the embodiment of the present invention, step S2 may be implemented as follows:
according to the cauchy-adama theorem: for univariate power series, as in equation (4), the convergence radius S r Comprises the following steps:
wherein, V i [n]Coefficient of nth order, S, being the coefficient of the power series of the i-voltage of the node r The convergence radius of the node voltage holomorphic function in the form of power series, namely the static voltage stability boundary of the power system.
Through step S2, power system quiescent voltage stabilization boundary S r Can be calculated by equation (5).
S3: the static voltage stability boundary is quickly and accurately calculated.
In the embodiment of the present invention, step S3 may be implemented as follows:
since the efficiency of calculating the static voltage stabilization boundary directly according to the cauchy-adama theorem is low, an analytic relation between the static voltage stabilization boundary and a ratio example of the coefficients of the front and rear terms of the node voltage power series is deduced below.
Firstly, defining the upper bound of the coefficient proportion of the front term and the rear term of the voltage power series as L:
wherein sup represents the upper bound when n tends to infinity, L is a finite quantity, V i [n]And V i [n+1]Are the nth order and (n +1) th order coefficients of the node voltage power series.
Then, given an arbitrarily small positive number ξ >0, there is n such that the following is satisfied:
then, like equation (7), the m-th order coefficient to the n-th order coefficient satisfy equation (8):
wherein m < n. Multiplying equation (8) yields:
finishing to obtain:
|V i [n]| 1/n ＜[|V i [m]|(L+ξ) -m ] 1/n (L+ξ) (10)
since xi is an arbitrarily small positive number, then taking the limits on both sides of equation (10) in conjunction with equation (6) yields:
similar to the derivation process of equations (6) to (11), for the lower limit of the ratio of coefficients of the terms before and after the voltage power series, we can obtain:
where inf represents the lower bound when n tends to infinity.
Combining equation (11) and equation (12) yields:
therefore, if the limit of the ratio of the coefficients of the preceding and following terms of the voltage power series exists, that is, equation (14) satisfies:
then from equation (13) and equation (14) we can derive:
in conjunction with equation (5), one can obtain:
wherein, V i [n]And V i [n+1]Coefficient of the nth and (n +1) th order of the node voltage power series, S r Is the power system static voltage stability boundary.
Through the step S3, the power system static voltage stability boundary can be calculated quickly and accurately.
The technical solution of the present invention is further specifically described by the embodiment in the IEEE 14 node standard power system shown in fig. 3 and with reference to the drawings.
First, according to the fully pure embedding method with the physical mapping factor introduced in the above step S1, the power flow balance equation of the IEEE 14 node standard power system in fig. 3 is solved to obtain an analytic expression in the form of a power series of the node voltage.
Then, an analytical expression of the static voltage stabilization boundary is derived based on the cauchy-adama theorem cited in the above-described step S2.
Finally, the static voltage stability boundary is calculated quickly and accurately according to the analytic relationship between the static voltage stability boundary and the coefficient ratio of the front and rear terms of the node voltage power series derived in the step S3. As shown in FIG. 4, the conventional Cauchy-Adama theorem, equation (5), still fails to converge to the quiescent voltage stability boundary value, S, until the 100 th order voltage power series coefficient r The proposed method of calculating the boundary of the quiescent voltage stability based on the all-pure embedding method, namely equation (16), can converge to the value of the quiescent voltage stability boundary S at the 40 th order voltage power series coefficient r 3.60, the proposed solution based on all-pure is demonstratedThe static voltage stability boundary calculation method of the embedding method can quickly and accurately calculate the static voltage stability boundary.
It should be noted that, according to the implementation requirement, each step/component described in the present application can be divided into more steps/components, and two or more steps/components or partial operations of the steps/components can be combined into new steps/components to achieve the purpose of the present invention.
Although the present invention makes more use of terms such as power system, all-pure embedding, power flow equations, power series coefficients, static voltage stability boundaries, analytical expressions, etc., the possibility of using other terms is not excluded. These terms are used merely to more conveniently describe and explain the nature of the present invention; they are to be construed as being without limitation to any additional limitations that may be imposed by the spirit of the present invention.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. A static voltage stability boundary calculation method based on an all-pure embedding method is characterized by comprising the following steps:
s1: solving a power flow balance equation of the power system by using a pure embedding method containing physical mapping factors to obtain an analytic expression in a node voltage power series form;
s2: deducing an analytical expression of the static voltage stability boundary based on the Cauchy-Adama theorem, namely deducing an analytical expression of the static voltage stability boundary of the power system by using a power series expression of the Cauchy-Adama theorem processing node voltage;
s3: calculating a voltage stability boundary according to an analytical expression of the static voltage stability boundary of the power system, specifically comprising:
s3.1: collecting power generation, load and network data of a power system;
s3.2: substituting power generation, load and network data of power system intoA power series expression of the node voltage is obtained by a power flow balance equation
S3.3: power series expression based on node voltage
Analytical expression based on static voltage stability boundary
Calculating S therein r I.e. the quiescent voltage stability boundary, V, of the power system i [n]Coefficient of the nth order, V, of the voltage power series of the node i i [n+1]Is the n +1 th order coefficient of the node i voltage power series, and s is a pure physical mapping factor.
2. The method according to claim 1, wherein step S1 includes:
s1.1: embedding a physical mapping factor in a power flow balance equation of the power system;
s1.2: solving a power flow balance equation of the electric power system containing the physical mapping factor by using a pure embedding method;
s1.3: and obtaining an analytic expression of the node voltage power series form.
3. The method of claim 2, wherein the equations are balanced in the original power flow
Embedding an all-pure physical mapping factor s to obtain a power flow balance equation containing the all-pure physical mapping factor s
Wherein, the device can be used for adjusting the running state of the power system,Y ik is an element of the ith row and kth column in the nodal admittance matrix, Y ik * Represents Y ik Conjugation of (b), P i And S i Active and complex power injection, V, representing node i i Is the voltage of node i, V i * Represents V i Conjugation of (2) V k Voltage of a node k adjacent to the node i, V k * Represents V k Conjugation of (2) V sw To balance the voltage of the node, | V i sp I represents a specific amplitude of the voltage of the PV generator node i, N is the total number of nodes of the power system, Q i Representing the reactive power injection quantity, V, of node i i (s) and Q i (s) all-pure functions of voltage and reactive power at node i, respectively, in the form of a power series, i.e.
4. The method of claim 3, wherein the coefficients of the same order s on both sides of the power flow balance equation with the fully-pure physical mapping factor s are equal in a one-to-one correspondence manner, so as to establish a recursion relationship between the current order coefficient (unknown quantity) and the previous order coefficient (known quantity) of the node voltage power series, namely V i [n]＝f(V i [0],…,V i [n-1]) N is not less than 1, wherein, V i [0],…,V i [n-1]The function f represents the node voltage as the 0 th order to (n-1) th order coefficients of the node i voltage power seriesA recursive relationship between power series coefficients, wherein a current order coefficient is an unknown quantity and a previous order coefficient is a known quantity.
5. The method of claim 4, wherein the 0 th order coefficient V of the i-node voltage power series is solved by substituting 0 into a power flow balance equation containing a fully pure physical mapping factor s i [0]Then, all coefficients V of the node i voltage power series can be obtained through the recursion relation f between the node voltage power series coefficients i [n]N is more than or equal to 1, so as to obtain the analytic expression of the power series form of the voltage of the node i
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