CN110571788A - static voltage stability domain boundary coefficient calculation method based on dynamic equivalent circuit - Google Patents
static voltage stability domain boundary coefficient calculation method based on dynamic equivalent circuit Download PDFInfo
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- H—ELECTRICITY
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Abstract
The invention discloses a static voltage stability domain boundary coefficient calculation method based on a dynamic equivalent circuit. Firstly, acquiring a weak voltage stabilization node through an online load impedance model margin index; then, obtaining voltage and current data of all nodes of the current power system by utilizing online measurement to obtain thevenin equivalent parameters of the power system, equating the power system to a two-node thevenin system by utilizing the thevenin equivalent parameters, obtaining a Taylor expansion of equivalent potential relative to control parameters, and arranging, thereby obtaining a static voltage stability region corresponding to the weak node of the current power system according to the essential condition of single-machine single-negative-charge voltage critical instability, the equivalent reactance and the equivalent potential in the thevenin system and the Taylor expansion; and finally, obtaining the boundary coefficient of the static voltage stable region corresponding to the weak node of the current power system.
Description
Technical Field
the invention belongs to the field of stability of power systems, and particularly relates to a method for calculating a static voltage stability domain boundary coefficient.
background
with the expansion of the interconnection scale of the regional power grid, the increasing of the power demand, the massive access of renewable energy power generation, the massive application of new energy vehicles, the gradual complexity of the power grid operation and the increasing of the risk of voltage instability of the power system, the voltage stability problem draws more and more attention.
At present, the main results of studying the stability of the static voltage are a maximum transmission power method based on a power flow equation, sensitivity analysis, power flow multi-solution analysis and the like, and the analysis methods are called point-by-point methods. However, with the wide application of the large-scale grid connection and demand side response technology of the distributed energy, the characteristics of intermittent property and strong randomness increase the uncertainty of the power increasing direction of the power system, so that the analysis method of the point-by-point method needs to perform repeated stability analysis aiming at all possible power increasing directions, which inevitably brings heavy calculation burden and is not beneficial to the safety monitoring, defense and control of the static voltage stability of the power system. And the Static Voltage Stability Region (SVSR) of the power system describes and determines the network topology structure and parameters through a concise explicit mathematical relationship, the system has an operation Region of Static Voltage Stability, and the Voltage Stability safety margin and the optimal control information of the system in the uncertain power increasing direction can be accurately provided through the relative relationship between the system operation point and the SVSR boundary, so that the online real-time safety monitoring, defense and control of the power system are more scientific and effective.
Currently, common methods for calculating SVSR boundaries include: the fitting method and the direct method. Because the injection space dimension of the actual power system is higher and the power increasing direction is uncertain, the number of critical points on the SVSR boundary to be searched is increased along with the dimension and the power increasing direction, so that the calculation amount for searching the SVSR boundary by the fitting method presents the exponential increasing trend, and the direct online calculation of the SVSR boundary of a large-scale system is difficult to realize. The direct method is to perform Taylor series expansion on a determinant of a Jacobian matrix of a trend equation near a critical point, and describe a domain boundary near the critical point approximately by using a quadratic polynomial of a nonlinear term. The hyperplane can describe local topological characteristics of the SVSR boundary on the premise of meeting the precision, but different key parameters and critical points have large influence on the SVSR boundary topological structure, and the high-order derivative of the load flow equation of the practical power system is difficult to directly solve, so that the application of the method in practice is limited.
disclosure of Invention
the voltage instability of an actual power system is mostly in a monotonic instability mode, so that the analysis method for the static voltage stability is widely applied. How to accurately and quickly construct the SVSR boundary becomes the key of the research of the static voltage safety domain. When constructing the SVSR boundary, how to determine the key parameters in the mathematical model becomes the focus of the current research.
In order to solve the above problems, the invention provides a method for calculating a static voltage stability domain boundary coefficient based on a dynamic equivalent circuit, which comprises the following steps:
Acquiring a weak voltage stabilization node through an online load impedance model margin index; the online load impedance module margin index expression is as follows:
In the formula (1), the reaction mixture is,for the impedance model margin index of the system node i at time t,representing the load reactance at point i of the system node at time t,Representing the equivalent reactance of a system node i at the time t; index of margin of impedance modeMaximum value of 1 whenWhen the voltage is higher than the threshold value, the current power system operates at a voltage stability critical point; when in useWhen the power system is in the unstable state, the power system represents the current power system is in the unstable state; calculating the impedance of all system nodesPerforming reverse sequencing after the modular margin indexes, and identifying two nodes with the minimum indexes as weak voltage stabilization nodes;
obtaining voltage and current data of all nodes of the current power system by utilizing online measurement to obtain thevenin equivalent parameters of the power system, and equating the power system into a two-node thevenin system by utilizing the thevenin equivalent parameters; in the Thevenin system, the equivalent reactance of a system node i issystem node i system side equipotential isfurther obtaining equivalent potential by the Jacobian matrix derivation of the power flow equationWith respect to the control parameter Δ Pkand Δ Qkand sorting the sorted Taylor expansion, wherein the sorted Taylor expansion is as follows:
In the formula (2), Δ Pkrepresenting the active power output change, Δ Q, of PQ and PV nodes in a power systemkRepresenting the reactive power output change of the PQ node in the power system,Representing the variation of the bus voltage of the PV node, ZLLijRepresenting the mutual impedance between system node i and system node j, Kij，λjk，ηjk，αjk，βjk，γjkRespectively representing the corresponding expansion coefficients in the Taylor formula;
step three, according to the sufficient condition of single-machine single-load voltage critical instability and the equivalent reactance in the Thevenin systemand the equivalent potentialAnd a Taylor expansion formula is adopted, and then a static voltage stable domain corresponding to the weak node of the current power system is obtained according to the formula (3);
The formula (3) can be finally arranged as:
In the formulae (3) and (4), PiAnd QiRespectively representing active injection and reactive injection, R, of a system node iL，XLAnd ZLRespectively representing the equivalent resistance value, reactance value and impedance value of the i Thevenin equivalent circuit system side of the system node, b1-b4Respectively representing the boundary coefficients of the static voltage stable domains;
step four, setting:Wherein epsiloniFor correcting the coefficient, the method is used for representing the disturbance of the system node i,For the current time t1The load impedance modulus margin at system node i,Is the last moment t0setting the load impedance model margin of a system node i according to the historical operating state of the power systemiMaximum value ofAnd minimum valueIf it isthe boundary coefficient of the static voltage stability domain corresponding to the weak node of the current power system, which is obtained in the third step, is the obtained value; otherwise, returning to the step one.
the invention provides a static voltage stability domain parameter calculation method based on a Thevenin dynamic equivalent circuit. Firstly, weak nodes influencing the voltage stability of a system are obtained through local online voltage stability indexes; secondly, measuring data in real time by using a wide area measurement system according to the equivalent method of wearing a Vietnam model to obtain a Thevenin equivalent model of the system; then, a Taylor analytic expression of the equivalent potential with respect to the control parameter variable is obtained by utilizing the Jacobi matrix; and obtaining an analytical expression of a static voltage stability domain of a general system by combining a critical condition of voltage stability according to the information of the current operating point and the relation of the equivalent potential on the control parameter variable.
Drawings
FIG. 1 is a Thevenin two-node system equivalent to a general power network;
FIG. 2 is a flow chart of the calculation of the boundary coefficient of the static voltage stability domain based on the dynamic equivalent circuit provided by the invention;
FIG. 3 is a diagram of IEEE39 node system connections according to an embodiment of the present invention;
FIG. 4 is the correlation gain between Bus21 and the load node in the embodiment;
FIG. 5 is a graph of the correlation gain between Bus21 and the generator node in the example;
FIG. 6 is a boundary error curve of the stable domain of the IEEE39 node system of the embodiment.
Detailed Description
The technical solution of the present invention is further described in detail with reference to the flow chart.
The invention relates to a method for calculating a static voltage stability domain boundary coefficient based on a dynamic equivalent circuit, which comprises the following steps,
acquiring a weak voltage stabilization node through an online load impedance model margin index; the online load impedance module margin index expression is as follows:
In the formula (1), the reaction mixture is,For the impedance model margin index of the system node i at time t,representing the load reactance at point i of the system node at time t,Representing the equivalent reactance of a system node i at the time t; index of margin of impedance modeMaximum value of 1 whenwhen the voltage is higher than the threshold value, the current power system operates at a voltage stability critical point; when in useWhen the power system is in the unstable state, the power system represents the current power system is in the unstable state; and calculating impedance mode margin indexes of all system nodes, and then sequencing in a reverse order, and identifying the two nodes with the minimum indexes as weak voltage stabilization nodes.
obtaining voltage and current data of all nodes of the current power system by utilizing online measurement to obtain thevenin equivalent parameters of the power system, and equating the power system to a two-node thevenin system by utilizing the thevenin equivalent parameters, wherein a specific equivalent circuit diagram is shown in figure 1; in the Thevenin system, the system side equivalent reactance of a system node i isSystem node i system side equipotential isFurther obtaining equivalent potential by the Jacobian matrix derivation of the power flow equationWith respect to the control parameter Δ PkAnd Δ QkAnd sorting the sorted Taylor expansion, wherein the sorted Taylor expansion is as follows:
in the formula (2), Δ PkRepresenting the active power output change, Δ Q, of PQ and PV nodes in a power systemkRepresenting the reactive power output change of the PQ node in the power system,Representing the variation of the bus voltage of the PV node, ZLLijRepresenting the mutual impedance between system node i and system node j, Kij，λjk，ηjk，αjk，βjk，γjkThe corresponding expansion coefficients in the Taylor formula are respectively represented.
Step three, according to the sufficient condition of single-machine single-load voltage critical instability and the equivalent reactance in the Thevenin systemAnd the equivalent potentialAnd a Taylor expansion formula is adopted, and then a static voltage stable domain corresponding to the weak node of the current power system is obtained according to the formula (3);
the formula (3) can be finally arranged as:
In formulae (3) and (4), PiAnd QiRespectively representing active injection and reactive injection, R, of a system node iL，XLAnd ZLAnd respectively representing an equivalent resistance value, a reactance value and an impedance value of the system node i Thevenin equivalent circuit system side. b1-b4The boundary coefficients of the static voltage stability domains are respectively represented.
Step four, setting:Wherein epsiloniFor correcting the coefficient, the method is used for representing the disturbance of the system node i,for the current time t1The load impedance modulus margin at system node i,Is the last moment t0setting the load impedance model margin of a system node i according to the historical operating state of the power systemiMaximum value ofAnd minimum valueIf it isThe boundary coefficient of the static voltage stability domain corresponding to the weak node of the current power system, which is obtained in the third step, is the obtained value; otherwise, returning to the step one.
The invention adopts IEEE39 node calculation example to verify the validity of the method provided by the invention. The wiring diagram is shown in fig. 3. And performing N-1 verification on the line of the network, selecting the most serious line 21-22 fault by taking the load margin as an index, and constructing the SVSR boundary. The specific load margin information is shown in table 1:
TABLE 1 load node impedance model margin information
and screening the load nodes Bus21 and Bus 23 with weakest voltage stability according to the load margin index. Selecting an SVSR boundary construction process corresponding to a load node BUS21 for example, selecting load nodes BUS 3, BUS 4, BUS 8, BUS15, BUS 16, BUS 18, BUS21 and BUS 26, selecting generator nodes BUS 33, BUS 34, BUS 35 and BUS 36 as key areas, and using corresponding control variables as parameter spaces.
Table 2 lists coefficients of SVSR boundary dimension reduction of the voltage stabilization weak node Bus21 in the node control parameter space of the key region.
TABLE 2 Voltage stabilization weak node Bus21 corresponding SVSR boundary results
FIG. 4 is the correlation gain between Bus21 and the load node in the embodiment; FIG. 5 is a graph of the correlation gain between Bus21 and the generator node in the example; fig. 6 shows an SVSR boundary error curve of the IEEE39 node system, and it can be seen that the errors of the SVSR boundary constructed by the analysis method provided by the present invention are all below 1% in the low-dimensional space. Fig. 6 shows that the SVSR boundary approximation analytical expression proposed in the present invention can better approximate the boundary. Although the boundary coefficient of the expression contains some secondary terms, coupling terms among different variables do not exist, and intuitive and useful operation safety information is provided for system operation scheduling personnel.
Further evaluating the efficiency of searching SVSR boundary by using the method provided by the invention, the arithmetic data adopted by the invention are all from Matpower 6.0.
TABLE 3 comparison of calculated times for different methods
Table 3 shows the calculation time (CPU Intel Core i5-4210H, main 2.9GHz and memory 8GB) for fitting SVSR boundary by adopting the method and CPF search provided by the invention. Tables 4-3 the results show that: the method for searching the SVSR boundary by using the CPF is lower in computational efficiency than the method provided by the invention. From the aspect of time consumption of calculation, the method disclosed by the invention completely meets the time requirement of online calculation of the SVSR boundary.
while the present invention has been described with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, which are illustrative only and not restrictive, and various modifications which do not depart from the spirit of the present invention and which are intended to be covered by the claims of the present invention may be made by those skilled in the art.
Claims (1)
1. A static voltage stability domain boundary coefficient calculation method based on a dynamic equivalent circuit is characterized by comprising the following steps:
Acquiring a weak voltage stabilization node through an online load impedance model margin index; the online load impedance module margin index expression is as follows:
In the formula (1), the reaction mixture is,For the impedance model margin index of the system node i at time t,Representing the load reactance at point i of the system node at time t,Representing the equivalent reactance of a system node i at the time t; index of margin of impedance modemaximum value of 1 whenWhen the voltage is higher than the threshold value, the current power system operates at a voltage stability critical point; when in usewhen the power system is in the unstable state, the power system represents the current power system is in the unstable state; calculating impedance mode margin indexes of all system nodes and then carrying out reverse sequencing, and identifying two nodes with the minimum indexes as weak voltage stabilization nodes;
Obtaining voltage and current data of all nodes of the current power system by utilizing online measurement to obtain thevenin equivalent parameters of the power system, and equating the power system into a two-node thevenin system by utilizing the thevenin equivalent parameters; in the Thevenin system, the equivalent reactance of a system node i isSystem node i system side equipotential isFurther obtaining equivalent potential by the Jacobian matrix derivation of the power flow equationWith respect to the control parameter Δ PkAnd Δ QkAnd sorting the sorted Taylor expansion, wherein the sorted Taylor expansion is as follows:
In the formula (2), Δ PkRepresenting the active power output change, Δ Q, of PQ and PV nodes in a power systemkRepresenting the reactive power output change of the PQ node in the power system,Representing the variation of the bus voltage of the PV node, ZLLijrepresenting the mutual impedance between system node i and system node j, Kij，λjk，ηjk，αjk，βjk，γjkRespectively representing the corresponding expansion coefficients in the Taylor formula;
Step three, according to the sufficient condition of single-machine single-load voltage critical instability and the equivalent reactance in the Thevenin systemAnd the equivalent potentialand a Taylor expansion formula is adopted, and then a static voltage stable domain corresponding to the weak node of the current power system is obtained according to the formula (3);
the formula (3) can be finally arranged as:
in the formulae (3) and (4), PiAnd Qirespectively representing active injection and reactive injection, R, of a system node iL，XLand ZLrespectively representing the equivalent resistance value, reactance value and impedance value of the i Thevenin equivalent circuit system side of the system node, b1-b4respectively representing the boundary coefficients of the static voltage stable domains;
Step four, setting:wherein epsilonifor correcting the coefficient, the method is used for representing the disturbance of the system node i,For the current time t1the load impedance modulus margin at system node i,Is the last moment t0Setting the load impedance model margin of a system node i according to the historical operating state of the power systemiMaximum value ofAnd minimum valueif it isthe boundary coefficient of the static voltage stability domain corresponding to the weak node of the current power system, which is obtained in the third step, is the obtained value; otherwise, returning to the step one.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112685981A (en) * | 2020-12-28 | 2021-04-20 | 南方电网科学研究院有限责任公司 | Static equivalence method and device for power system, terminal equipment and storage medium |
| CN113258580A (en) * | 2021-05-31 | 2021-08-13 | 山东大学 | Method and system for determining regulation sensitivity of voltage stability index of PQ node of alternating current-direct current power grid |
| CN115912384A (en) * | 2022-12-21 | 2023-04-04 | 国网湖北省电力有限公司经济技术研究院 | Voltage stabilization method for improving system containing high-proportion new energy at extra-high voltage direct current receiving end |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112685981A (en) * | 2020-12-28 | 2021-04-20 | 南方电网科学研究院有限责任公司 | Static equivalence method and device for power system, terminal equipment and storage medium |
| CN112685981B (en) * | 2020-12-28 | 2024-05-07 | 南方电网科学研究院有限责任公司 | Static equivalence method and device for power system, terminal equipment and storage medium |
| CN113258580A (en) * | 2021-05-31 | 2021-08-13 | 山东大学 | Method and system for determining regulation sensitivity of voltage stability index of PQ node of alternating current-direct current power grid |
| CN113258580B (en) * | 2021-05-31 | 2023-05-05 | 山东大学 | Method and system for determining voltage stability index regulation sensitivity of PQ node of AC/DC power grid |
| CN115912384A (en) * | 2022-12-21 | 2023-04-04 | 国网湖北省电力有限公司经济技术研究院 | Voltage stabilization method for improving system containing high-proportion new energy at extra-high voltage direct current receiving end |
| CN115912384B (en) * | 2022-12-21 | 2024-05-28 | 国网湖北省电力有限公司经济技术研究院 | Method for improving voltage stability of extra-high voltage direct current receiving end system containing high proportion new energy |
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