CN107658881A - Voltage stability critical point determination methods based on Thevenin's equivalence method - Google Patents
Voltage stability critical point determination methods based on Thevenin's equivalence 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
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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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Abstract
The invention discloses a kind of voltage stability critical point determination methods based on Thevenin's equivalence method, its step is：S1：It is a two node Thevenin's equivalence models by system equivalent；S2：According to Thevenin's equivalence model, the metric data and Thevenin's equivalence parameter of load bus are drawn, establishes measurement matrix equation；S3：Thevenin's equivalence parameter is solved：According to measurement matrix equation, state equation, using recurrent least square method, the recursive expression of the quantity of state of Thevenin's equivalence parameter is solved, updates quantity of state；S4：Residual equation is drawn according to state equation, using the uncertainty of Linear Estimation quantity of state, detection process is carried out to the false data of metric data；S5：According to throttled orifice is waited, evaluation index is established, and voltage stability critical point is judged.The present invention has a good precision, and suitable for transient process under large disturbances Thevenin's equivalence parameter calculating；Fast and effeciently online real-time tracking Thevenin's equivalence parameter.
Description
Technical Field
The invention relates to the field of voltage stability analysis and control of an electric power system, in particular to a voltage stability critical point judgment method based on a Thevenin equivalent method.
Background
With the rapid increase of the power demand, the acceleration of the interconnection process between power grids and the successive operation of the extra-high voltage alternating current and direct current project, the operation mode of the power system is more variable and complex, and the power system gradually approaches to the voltage stable operation boundary.
In the voltage stability analysis and control of the power system, the calculation of the voltage collapse point plays an extremely important role. A ground state power system is given, a mode that a load and a generator are synchronously increased is given, and a critical point of static voltage collapse can be estimated by using a continuous power flow method, so that a stability margin is determined, and system scheduling and operation are guided. However, this method has a problem of non-convergence near the critical point, it is difficult to obtain an accurate collapse point, and the amount of calculation is considerable as the system scale is enlarged. Therefore, it is important to find a method for rapidly and effectively determining the voltage stability threshold.
The voltage collapse of the power system is concealed and sudden, but research finds that the stability of the whole system is often closely related to the stability of a certain node or a certain area. By adopting the Thevenin equivalent method facing to the load nodes, the system network can be effectively simplified, the voltage stability of a certain load node can be quickly analyzed, the mechanism is simple, and the physical significance is clear, so that more and more attention is paid. In addition, the Thevenin equivalent method can also be used for searching voltage weak nodes in a complex system, thereby providing important basis for operation and regulation of the system.
In the early 90 s of the 20 th century, the successful development of Phasor Measurement Units (PMUs) based on the Global Positioning System (GPS) marked the emergence of the synchrophasor technology. Under the support of a high-speed communication network, data with time scales acquired by each PMU can be transmitted to a data center station with smaller delay to complete synchronous processing and analysis, thereby forming a Wide Area Measurement System (WAMS). Therefore, the method has important practical significance and research prospect for carrying out online analysis and monitoring on the system voltage stability by utilizing the synchronous data of the wide-area measurement system.
Disclosure of Invention
The invention aims to provide a method for judging a voltage stability critical point based on a Thevenin equivalent method, which is a Thevenin equivalent parameter tracking algorithm of time domain simulation, has good precision and is suitable for calculating Thevenin equivalent parameters in a transient process under large disturbance.
In order to achieve the purpose, the method for judging the voltage stabilization critical point based on the Thevenin equivalent method comprises the following steps:
s1: equating the system to a two-node Thevenin equivalent model;
s2: according to the two-node Thevenin equivalent model, based on data acquisition of a phasor measurement unit, obtaining measurement data and Thevenin equivalent parameters of the load nodes, and establishing a measurement matrix equation of the measurement data of the load nodes;
s3: solving the Thevenin equivalent parameters: obtaining a state equation of the Thevenin equivalent model according to the measurement matrix equation, solving a recursive expression of the state quantity of the Thevenin equivalent parameter by using a recursive least square method, and updating the state quantity of the state equation;
s4: obtaining a corresponding residual equation according to a state equation of the Thevenin equivalent model, and detecting and processing the false data of the measurement data of the load nodes by using the uncertainty of the linear estimation state quantity according to the state quantity of the state equation;
s5: and establishing an evaluation index according to the equal impedance model criterion, the load equivalent impedance model and the Thevenin equivalent impedance model, and judging the voltage stabilization critical point.
Preferably, in the step S1, the two-node thevenin equivalent model method includes: the rest part of the power grid except the nodes in the system is expressed by Thevenin equivalence, an equivalent voltage source and an equivalent impedance; and for any moment k, looking into the system from a certain load node, the system equivalent is a two-node Thevenin equivalent model.
Preferably, in step S2, in the two-node thevenin equivalent model, the measurement data of the load node includes a measured voltage phasor of the load node at time kAnd current phasor of load node at time kThevenin equivalent parameters comprise thevenin equivalent potential at k momentAnd Thevenin equivalent impedance Z k ；
The circuit theory can obtain:
equation (1) is expressed in complex form:
in the formula, V Rk For measuring voltage phasorsReal part of (jV) Ik For measuring voltage phasorsAn imaginary part of (a); e Rk To an equal potentialReal part of, jE Ik To an equal potentialExcess and deficiency of (C), R Tk Is an equivalent impedance Z k Real part of (jX) Tk Is an equivalent impedance Z k An imaginary part of (d); i is Rk Is a current phasorReal part of, jI Ik Is a current phasorAn imaginary part of (d);
the measured data of the load nodes and the real part and the imaginary part of thevenin equivalent parameters are disassembled, and the real part and the imaginary part of thevenin equivalent parameters are processedWriting into matrix form to obtain the measured data quantity of load nodeMeasuring a matrix equation;
for the k-th group of measured data in any data windowAndassuming that the Thevenin equivalent parameter value is unchanged; and selecting a proper data window length to simultaneously measure an equation.
Preferably, in the step S3, a specific process of solving the thevenin equivalent parameter is as follows: writing the measurement matrix equation into a state equation form of the Thevenin equivalent model:
y k ＝H k x k +ε k (4)
wherein, y k ＝[V Rk V Ik ] T ，x k ＝[E Rk E Ik R Tk X Tk ] T ，y k Matrix representing the real and imaginary components of the voltage in the load node measurement data, x k Representing the state quantity of the DeThevenin equivalent parameter at the k moment; h k Is with x k A corresponding iteration matrix; epsilon k Due to uncertainty of load node measurement data and errors caused by bad data;
using recursive least squares, the state quantity x at time k k The recursive expression of (c) is:
wherein, G k ,H k And P k Are all overlappedGeneration matrix for updating state quantity x k ；x k-1 Is the state quantity at the time k-1, P k-1 Is the corresponding iterative matrix at the time k-1, I represents the current;
selecting a proper measurement length K, wherein a specific algorithm is as follows:
a. initializing data: x is the number of 0 ＝[1 0 0 0] T ，P 0 ＝aI 4 ，a>, 0; wherein x is 0 Is in an initial state, p 0 An iteration matrix P in the initial state k A is a selected constant value;
b. for K =1,2, \ 8230;, K, intermediate quantities were calculatedAnd updating the iteration matrix G k Let G be k ＝P k-1 H k S k ；
c. Updating an iteration matrix P k To makeThe iteration state quantity x at the current time k k Satisfy the requirements of
For load node impedanceSatisfy the requirements of
Preferably, in step S4, uncertainty of the measurement data of the load node may have an influence on thevenin equivalent parameters, and the specific analysis method includes:
the state equation of the Thevenin equivalent model is y k ＝H k x k +ε k (ii) a Wherein epsilon k Representing errors caused by uncertainty of the load node measurement data and bad data;
the residual equation can be obtained:
r(x)＝y-Hx (6)
wherein r (x) is an error caused by uncertainty of the measured data and bad data;
note the bookRespectively represent the measured data V Rk 、V Ik 、I Rk 、I Ik Respectively corresponding real or imaginary components of the image,representing the state estimator x in the data window at time k k Uncertainty of (d); memory M K ＝{V Rk ,V Ik ,I Rk ,I Ik L K =1,2, \8230 |, K is a set of all measured data from the beginning until the end to the time K, representing uncertainty of state quantity by linear estimationComprises the following steps:
wherein M is belonging to the set M k Any one of the measured data, σ m Representing an uncertainty amount corresponding to the metrology data m; { R, I } denotes a set containing either real or imaginary parts of metrology data; β is an element of the set { R, I }; i is βj The imaginary part of the measured data represented by beta at the moment j is represented;is I βj An uncertainty representing an imaginary part of the metrology data; v βj Representing the real part of the measured data represented by beta at the moment j; delta Vβj Is a V βj An uncertainty amount of a real part of the representative metrology data; and j is between 1 and K.
Preferably, in the step S5, the criterion of the equal impedance mode is: when the load equivalent impedance mode is equal to the Thevenin equivalent impedance mode, the load power reaches the limit and corresponds to the stable critical point of the static voltage;
establishing an impedance mode ratio and an impedance mode margin to monitor whether the system reaches a voltage stability critical point or not according to the load equivalent impedance mode and the Thevenin equivalent impedance mode;
when the evaluation index is the impedance modulus ratio:
impedance-mode ratio alpha = | Z t,Thev |/|Z t,Li L, wherein l Z t,Thev I is the Thevenin equivalent impedance mode, | Z t,Li I is a load equivalent impedance mode; when the impedance mode ratio alpha tends to 1, the closer the system is to the voltage stabilization critical point; when the impedance mode ratio alpha =1, the system operation state is at a voltage stabilization critical point; when the alpha is smaller, the voltage of the load node is more stable;
when the evaluation index is the impedance mode margin:
impedance mode margin | Δ Z | = (| Z | =) t,Li |-|Z t,Thev |)/|Z t,Li When the impedance mode margin | Δ Z | tends to 0, the closer the system is to the voltage stabilization critical point; when the impedance module margin | delta Z | =0, the system operation state is at a voltage stabilization critical point; the larger the impedance mode margin | Δ Z | is, the more stable the node voltage is.
Preferably, in step S5, the weak node in the system is determined according to the impedance mode ratio or the impedance mode margin, specifically:
after Thevenin equivalence is carried out on the system, voltage stability analysis and identification of voltage weak nodes are carried out by calculating singular values of single load nodes; calculating a load flow Jacobian matrix according to the two-node Thevenin equivalent modelWherein:
wherein, A, O, C and D are respectively the first-order polarization conductors of active power and phase angle in the Jacobian matrixThe device comprises a matrix, a sub-matrix of first-order partial derivatives of active power and voltage, a sub-matrix of first-order partial derivatives of reactive power and phase angle, and a sub-matrix of first-order partial derivatives of reactive power and voltage; p is L 、Q L Respectively the active power and the reactive power of the load; p 1 、Q 1 Respectively equal active power and reactive power; e s Is the amplitude of the equivalent voltage; delta. For the preparation of a coating 1 Is the phase angle of the equivalent voltage; p is 2 、Q 2 Respectively the active power and the reactive power of the load nodes; (ii) a U shape L Is the magnitude of the load node voltage, delta 2 Is the phase angle of the load node voltage; g is the equivalent conductance; b is equivalent susceptance;
and then solving singular values of the Jacobian matrix, comparing the singular values, and finding out the minimum singular value, wherein the corresponding node is the weakest node.
Compared with the prior art, the invention has the following beneficial effects:
(1) According to the method, a complex and huge system is simplified into a simple two-node system mainly through Thevenin equivalence, and the voltage stability and the critical operation condition of a load node are analyzed by using an equal impedance mode criterion; the method has good precision, and is suitable for calculating Thevenin equivalent parameters in the transient process under large disturbance.
(2) According to the method, the equivalent impedance of the power grid side is calculated by using a recursive least square method based on PMU (phasor measurement Unit) measurement data according to the voltage and current phasor characteristics of the power grid node, thevenin equivalent parameters can be quickly and effectively tracked on line in real time, and a voltage stability critical point judgment index is further provided.
Drawings
FIG. 1 is a two-node Thevenin equivalent model diagram of the present invention;
FIG. 2 is a diagram of Thevenin equivalent results with bad data according to the present invention;
FIG. 3 is a schematic diagram of a two-node system of the present invention;
FIGS. 4a and 4b are schematic diagrams of node 15 Thevenin equivalent results of the IEEE-39 system of the present invention.
Detailed Description
The invention provides a method for judging a voltage stabilization critical point based on a Thevenin equivalent method, which is further explained with reference to the attached drawings and specific embodiments in order to make the invention more obvious and understandable.
The invention relates to a voltage stability analysis and monitoring method of a wide-area measurement system based on Thevenin equivalence, which mainly comprises the following steps:
looking into the system from a certain load node, equating the whole system to be a simple two-node system;
in an actual power grid, the power grid outside a specified load node configured with PMU (Phasor Measurement Unit) can be regarded as a black box, and according to the circuit principle, the rest of the power grid outside the node is represented by thevenin equivalent, that is, an equivalent voltage source and an equivalent impedance. For any time k, looking into the system from a certain load node, the whole system can be equivalent to a simple two-node system.
And secondly, evaluating the voltage stability through various voltage stability indexes. The details are as follows:
as shown in fig. 1, a two-node thevenin equivalent model, in which,for the measured voltage phasor of the load node at time k,the current phasor at the load node at time k,is thevenin equivalent potential at time k, Z k Is thevenin equivalent impedance at the time k.
The circuit theory can obtain:
equation (1) is expressed in complex form:
in the formula, V Rk For measuring voltage phasorsReal part of, jV Ik For measuring voltage phasorsAn imaginary part of (a); e Rk To an equal potentialReal part of (jE) Ik To an equal potentialExcess and deficiency of (C), R Tk Is an equivalent impedance Z k Real part of (jX) Tk Is an equivalent impedance Z k An imaginary part of (d); i is Rk Is a current phasorReal part of, jI Ik Is a current phasorThe imaginary part of (c).
The real part and the imaginary part of the measured data are separated, andwritten in matrix form, the following measurement matrix equation can be obtained:
for the k-th group of measured data in any data windowAndassuming that thevenin equivalent parameter values are unchanged. The measurement equations are combined by selecting a proper data window length, and thevenin equivalent parameters can be estimated by a mathematical method.
Thevenin equivalent parameter solving is carried out by a least square method, and the specific process is as follows:
the measurement matrix equation is written in the form of the following equation of state:
y k ＝H k x k +ε k (4)
wherein, y k ＝[V Rk V Ik ] T ，x k ＝[E Rk E Ik R Tk X Tk ] T ，y k Matrix, x, representing real and imaginary components of voltage in load node metrology data k Representing the state quantity of thevenin equivalent parameters at the k moment; h k Is with x k A corresponding iteration matrix; epsilon k Due to uncertainty in PMU measurement data and errors caused by bad data.
For equation (4), recursive least squares (The recursive least square RLS) can be used, and The state quantity x at time k k The recursive expression of (c) is:
wherein G is k ,H k And P k Are all iterative matrices for updating the state quantity x k ；x k-1 Is the state quantity at the time k-1, P k-1 At time k-1The corresponding iterative matrix, I, represents the current.
Selecting a proper measurement length K, wherein the specific algorithm is as follows:
(a) Initializing data: x is the number of 0 ＝[1 0 0 0] T ，P 0 ＝aI 4 ，a>, 0; wherein x is 0 Is in an initial state, p 0 The iteration matrix P in the initial state k A is a selected constant value.
(b) For K =1,2, \ 8230;, K, intermediate quantities were calculatedAnd updating the iteration matrix G k Let G be k ＝P k-1 H k S k ；
(c) Updating an iteration matrix P k To makeThe iteration state quantity x at the current time k k Satisfy the requirement of
For load node impedance, satisfyAnd further analyzing the voltage stability and the breakdown point according to the equal impedance mode criterion.
The PMU data uncertainty affects the peer-to-peer parameters, and the specific analysis is as follows:
the equation of state of the Thevenin equivalent model is y k ＝H k x k +ε k In which epsilon k The error caused by uncertainty of PMU measurement data and bad data is shown; the residual equation can be obtained:
r(x)＝y-Hx (6)
where r (x) is the error due to uncertainty in PMU measurement data and bad data.
In the existing voltage stability analysis research, PMU data is mostly processed into white Gaussian noise with small variance, but when a significant error (such as pulse noise, data asynchronism, network attack and the like) occurs, the significant error of Thevenin equivalent parameters can be caused, and thus errors of voltage stability and breakdown point judgment are caused.
Note the bookRespectively representing PMU measurement data V Rk 、V Ik 、I Rk 、I Ik Respectively corresponding real or imaginary parts of the image,representing the state estimator x in the current time k data window k Uncertainty of (d); memory M K ＝{V Rk ,V Ik ,I Rk ,I Ik I K =1,2, \ 8230;, K } is the set of all measured data from the beginning until the end to the time K, then the uncertainty of the state quantity is represented by a linear estimationComprises the following steps:
wherein M is belonging to the set M k Any one of the measured data, σ m Representing an uncertainty amount corresponding to the metrology data m; { R, I } denotes a set containing real or imaginary parts of PMU metrology data; β is an element of the set { R, I }; i is βj The imaginary part of the measured data represented by beta at the moment j is represented;is I βj An uncertainty representing an imaginary part of the metrology data; v βj Representing the real part of the measured data represented by beta at the moment j; delta Vβj Is a V βj An uncertainty amount of a real part of the representative metrology data; and j is between 1 and K.
When bad data (i.e. false data) exists in the data, if an attacker initiates data attack under the condition of a known system structure and state equation, an extreme condition occurs to an equivalent result.
As shown in fig. 2, the abscissa represents the load increase rate (%), and the ordinate represents the impedance value. Where the curve L1 is a relationship curve of load increase and thevenin equivalent impedance solved by a Robust recursive least squares method ((Robust RLS)), the curve L2 is a relationship curve of load increase and thevenin equivalent impedance solved by a recursive least squares method (RLS), and the curve L2 is a portion overlapping the curve L1. Curve L3 is the load increase versus the equivalent impedance of the load node.
When the load increase rate is 183%: the ordinate of the curve L2 is equal to the ordinate of the curve L3, while the ordinate of the curve L1 is smaller than the ordinate of the curve L3. At this time, the voltage instability of the system is judged when the Thevenin equivalent solved by the recursive least square method is used, and the actual system is stable, or; thevenin equivalent value solved by the recursive least square method judges that the system is stable and actually reaches a voltage collapse point.
Therefore, the detection and processing of bad spurious data in the metrology data of the power system remains an important direction for power system state estimation and analysis.
In the invention, the method for judging the voltage stabilization critical point based on thevenin equivalence comprises the following steps:
(1) Determination of voltage stability threshold
According to the equal impedance model criterion, when the load equivalent impedance model is equal to the system Thevenin equivalent impedance model, the load power reaches the limit, and the load power corresponds to the static voltage stability critical point. Therefore, the voltage stability critical point can be judged directly by comparing the load equivalent impedance mode with the system Thevenin equivalent impedance mode.
According to the load equivalent impedance mode and the system Thevenin equivalent impedance mode, various indexes such as impedance mode ratio, impedance mode margin and the like can be established to monitor whether the system reaches a voltage stability critical point.
(a) Impedance to mode ratio
Defining an impedance-to-mode ratio α = | Z t,Thev |/|Z t,Li L, wherein l Z t,Thev I is Thevenin equivalent impedance mode, | Z t,Li And | is the load equivalent impedance mode. When the impedance mode ratio alpha tends to 1, the system is closer to the voltage stabilization critical point; when the impedance mode ratio α =1, the system operation state is just at the voltage stabilization critical point. So the voltage at the load node is more stable as α is smaller.
(b) Margin of impedance mode
Defining an impedance modulus margin | Δ Z | = (| Z |) t,Li |-|Z t,Thev |)/|Z t,Li When the impedance mode margin | Δ Z | tends to 0, the system gets closer to the voltage stability critical point; when the impedance mode margin | Δ Z | =0, the system operation state is just at the voltage stabilization critical point. Compared with the impedance mode alpha, the impedance mode margin | Δ Z | can reflect how far the node is "away" from the critical point in the normal operating state, and the larger the impedance mode margin | Δ Z | is, the more stable the node voltage is.
In addition, other similar indexes can be established, but the essential is that the voltage stability critical point of the system is judged by adopting an equal impedance mode criterion.
(2) Identification of voltage weaknesses
Theoretically, according to two indexes of the impedance mode ratio or the impedance mode margin, which nodes in the system have weaker voltage can be judged (namely, the impedance mode ratio is larger or the impedance mode margin is smaller than the load node).
From another point of view, after Thevenin equivalence is carried out on the system, the network structure is greatly simplified, the calculation dimension is greatly reduced, and therefore voltage stability analysis and identification of voltage weak nodes can be carried out by calculating singular values of single load nodes.
FIG. 3 is a schematic diagram of a two-node system, which can calculate a power flow Jacobian matrix, which is a power flow Jacobian matrix Wherein:
a, O, C and D are respectively a first-order partial derivative sub-matrix of active power and phase angle, a first-order partial derivative sub-matrix of active power and voltage, a first-order partial derivative sub-matrix of reactive power and phase angle and a first-order partial derivative sub-matrix of reactive power and voltage in the Jacobian matrix; p L 、Q L Respectively the active power and the reactive power of the load; p 1 、Q 1 Respectively equal active power and reactive power; e s Is the amplitude of the equivalent voltage; delta. For the preparation of a coating 1 Is the phase angle of the equivalent voltage; p is 2 、Q 2 Respectively the active power and the reactive power of the load nodes; (ii) a U shape L The magnitude of the load node voltage, delta 2 Is the phase angle of the load node voltage; g is the equivalent conductance; and B is equivalent susceptance.
Therefore, in any running state, thevenin equivalence is carried out on all load nodes of the system, then an equivalent Jacobian matrix is calculated, singular values of the Jacobian matrix are solved, finally the minimum singular value is found through comparison, and the corresponding node is the weakest node.
Illustratively, computational analysis may be performed on the IEEE-39 node system in order to verify the equivalent accuracy and validity of the proposed algorithm. Fig. 4a and 4b are diagrams of thevenin equivalent results of node No. 15 in IEEE-39. In the IEEE-39 node system, the growth method is set as follows: the power of all loads in the system (the power factor remains the same as the initial state) and the active power of the generator all increase in the same proportion until the power flow no longer converges.
As shown in fig. 4a, the abscissa indicates the load increase exponent λ, and the ordinate indicates the impedance value. Wherein, the curve S1 represents the variation trend of thevenin equivalent impedance, and the curve S2 represents the variation trend of load impedance. In the curve S1, when the load increase index lambda is gradually increased, the value of thevenin equivalent impedance is gradually reduced; in the curve S2, when the load increase index λ gradually increases, the value of the load impedance gradually increases; and thevenin equivalent impedance is smaller than the value of the load impedance.
Fig. 4b is a diagram showing a variation curve of the impedance mode ratio and the load increase exponent λ, the abscissa is the load increase exponent λ, and the ordinate is the value of the impedance mode ratio. When the load increase exponent λ is gradually increased, the value of the impedance-mode ratio is gradually increased from 0 to approximately 1, and the value of the impedance-mode ratio is always between 0 and 1. That is, when the power flow of the system cannot be converged (the heavy load voltage collapses), the thevenin equivalent impedance mode and the load impedance mode are approximately equal within an error range, that is, the impedance mode ratio is about 1.
If thevenin equivalence is carried out on all load nodes in the system, and the voltage critical index is calculated, the corresponding node with obvious index change is the weakest node when the system is close to the voltage stabilization critical point. The system also considers the influence of noise errors in the data transmission process and larger errors caused by equivalent results such as impulse noise, data asynchronism, network attack and the like.
The method for judging the voltage stability critical point of the Thevenin equivalent parameters is still applicable to a large system, can identify the node with weak voltage while judging the voltage stability critical point of the system, and can provide reference basis for operation planning, off-line calculation, accident analysis and the like of a power system.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.
Claims (7)
1. A method for judging a voltage stabilization critical point based on a Thevenin equivalent method is characterized by comprising the following steps:
s1: the system equivalence is a two-node Thevenin equivalent model;
s2: according to the two-node Thevenin equivalent model, based on data acquisition of a phasor measurement unit, obtaining measurement data and Thevenin equivalent parameters of the load nodes, and establishing a measurement matrix equation of the measurement data of the load nodes;
s3: solving the Thevenin equivalent parameters: obtaining a state equation of the Thevenin equivalent model according to the measurement matrix equation, solving a recursive expression of the state quantity of the Thevenin equivalent parameter by using a recursive least square method, and updating the state quantity of the state equation;
s4: obtaining a corresponding residual equation according to a state equation of the Thevenin equivalent model, and detecting and processing the false data of the measurement data of the load nodes by using the uncertainty of the linear estimation state quantity according to the state quantity of the state equation;
s5: and establishing an evaluation index according to the equal impedance model criterion, the load equivalent impedance model and the Thevenin equivalent impedance model, and judging the voltage stabilization critical point.
2. The method for determining the voltage stabilization critical point based on the Thevenin equivalent method as claimed in claim 1,
in the step S1, the two-node thevenin equivalent model method includes: the rest part of the power grid except the nodes in the system is expressed by Thevenin equivalence, an equivalent voltage source and an equivalent impedance; and for any moment k, looking into the system from a certain load node, the system equivalent is a two-node Thevenin equivalent model.
3. The method for determining the voltage stabilization critical point based on the Thevenin equivalent method as claimed in claim 2,
in step S2, in the two-node thevenin equivalent model, the measurement data of the load node includes a measurement voltage phasor of the load node at the time kAnd current phasor of load node at time kThevenin equivalent parameters comprise thevenin equivalent potential at k momentAnd Thevenin equivalent impedance Z k ；
The circuit theory can obtain:
equation (1) is expressed in complex form:
in the formula, V Rk For measuring voltage phasorsReal part of, jV Ik For measuring voltage phasorsAn imaginary part of (a); e Rk Is equal potentialReal part of, jE Ik To an equal potentialExcess and deficiency of (C), R Tk Is an equivalent impedance Z k Real part of, jX Tk Is an equivalent impedance Z k An imaginary part of (a); i is Rk Is a current phasorReal part of, jI Ik Is a current phasorAn imaginary part of (d);
the measured data of the load nodes and the real part and the imaginary part of thevenin equivalent parameters are disassembled, and the real part and the imaginary part of thevenin equivalent parameters are processedWriting the measurement matrix into a matrix form to obtain a measurement matrix equation of the measurement data of the load node;
for kth group of measured data in arbitrary data windowAndassuming that the Thevenin equivalent parameter value is unchanged; and selecting a proper data window length to simultaneously measure an equation.
4. The method for determining the voltage stabilization critical point based on the Thevenin equivalent method as claimed in claim 3,
in the step S3, the specific process of solving the thevenin equivalent parameter is as follows:
writing the measurement matrix equation into a state equation form of the Thevenin equivalent model:
y k ＝H k x k +ε k (4)
wherein, y k ＝[V Rk V Ik ] T ，x k ＝[E Rk E Ik R Tk X Tk ] T ，y k Matrix representing real and imaginary components of voltage in load node measurement data, x k Representing the state quantity of the DeThevenin equivalent parameter at the k moment; h k Is with x k A corresponding iteration matrix; epsilon k The errors are caused by uncertainty of measurement data of the load nodes and bad data;
using recursive least squares, the state quantity x at time k k The recursive expression of (c) is:
wherein G is k ,H k And P k Are all iterative matrices for updating the state quantity x k ；x k-1 Is the state quantity at the time k-1, P k-1 I represents the current for the corresponding iterative matrix at the time k-1;
selecting a proper measurement length K, wherein the specific algorithm is as follows:
a. initializing data: x is the number of 0 ＝[1 0 0 0] T ，P 0 ＝aI 4 ，a>, 0; wherein x is 0 Is in an initial state, p 0 The iteration matrix P in the initial state k A is a selected constant value;
b. for K =1,2, \8230;, K, the intermediate quantity is calculatedAnd updating the iteration matrix G k Let G be k ＝P k- 1 H k S k ；
c. Updating an iteration matrix P k To makeThe iteration state quantity x at the current time k k Satisfy the requirement of
For load node impedanceSatisfy the requirements of
5. The method for determining a voltage stability critical point based on Thevenin equivalent method as defined in claim 4,
in step S4, uncertainty of the load node measurement data may affect thevenin equivalent parameters, and the specific analysis method is as follows:
the state equation of the Thevenin equivalent model is y k ＝H k x k +ε k (ii) a Wherein epsilon k Representing errors caused by uncertainty of the load node measurement data and bad data;
the residual equation can be obtained:
r(x)＝y-Hx (6)
wherein r (x) is an error caused by uncertainty of the measured data and bad data;
note bookRespectively represent the measured data V Rk 、V Ik 、I Rk 、I Ik Respectively corresponding real or imaginary components of the image,representing the state estimator x in the data window at time k k (ii) uncertainty of (d); memory M K ＝{V Rk ,V Ik ,I Rk ,I Ik I K =1,2, \ 8230;, K } is the set of all measured data from the beginning until the end to the K time, representing the uncertainty of the state quantity using linear estimationComprises the following steps:
wherein M is belonging to the set M k Any one of the measured data, σ m Representing an uncertainty amount corresponding to the metrology data m; { R, I } denotes a set containing either real or imaginary parts of metrology data; β is an element of the set { R, I }; I.C. A βj The imaginary part of the measured data represented by beta at the moment j is represented;is shown as I βj An uncertainty representing an imaginary part of the metrology data; v βj Representing the real part of the measured data represented by beta at the moment j;is a V βj An uncertainty amount of a real part of the representative metrology data; and j is between 1 and K.
6. The method for determining the voltage stabilization critical point based on the Thevenin equivalent method as claimed in claim 5,
in step S5, the criteria of the equal impedance mode are: when the load equivalent impedance mode is equal to the Thevenin equivalent impedance mode, the load power reaches the limit and corresponds to the static voltage stability critical point;
according to the load equivalent impedance model and the Thevenin equivalent impedance model, establishing an impedance model ratio and an impedance model margin to monitor whether the system reaches a voltage stabilization critical point;
when the evaluation index is the impedance modulus ratio:
impedance-mode ratio alpha = | Z t,Thev |/|Z t,Li L, wherein l Z t,Thev I is Thevenin equivalent impedance modulus,/| Z t,Li I is a load equivalent impedance mode; when the impedance mode ratio alpha tends to 1, the closer the system is to the voltage stabilization critical point; when the impedance mode ratio alpha =1, the system operation state is at a voltage stabilization critical point; when the alpha is smaller, the voltage of the load node is more stable;
when the evaluation index is the impedance mode margin:
impedance mode margin | Δ Z | = (| Z | =) t,Li |-|Z t,Thev |)/|Z t,Li When the impedance mode margin | Δ Z | tends to 0, the closer the system is to the voltage stabilization critical point; when the impedance module margin | delta Z | =0, the system operation state is at a voltage stabilization critical point; the larger the impedance mode margin | Δ Z | is, the more stable the node voltage is.
7. The method for determining the voltage stabilization critical point based on the Thevenin equivalent method as claimed in claim 6,
in step S5, a weak node in the system is determined according to the impedance mode ratio or the impedance mode margin, specifically:
after the system performs Thevenin equivalence, analyzing the voltage stability and identifying voltage weak nodes by calculating the singular value of a single load node; calculating a load flow Jacobian matrix according to the two-node Thevenin equivalent modelWherein:
a, O, C and D are respectively a first-order partial derivative sub-matrix of active power and phase angle, a first-order partial derivative sub-matrix of active power and voltage, a first-order partial derivative sub-matrix of reactive power and phase angle and a first-order partial derivative sub-matrix of reactive power and voltage in the Jacobian matrix; p L 、Q L Are respectively provided withActive power and reactive power for the load; p 1 、Q 1 Respectively equal active power and reactive power; e s Is the amplitude of the equivalent voltage; delta 1 Is the phase angle of the equivalent voltage; p is 2 、Q 2 Respectively the active power and the reactive power of the load nodes; (ii) a U shape L The magnitude of the load node voltage, delta 2 Is the phase angle of the load node voltage; g is the equivalent conductance; b is equivalent susceptance;
and then solving singular values of the Jacobian matrix, comparing the singular values, and finding out the minimum singular value, wherein the corresponding node is the weakest node.
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