CN104240151B - A kind of optimal corrective control of electric power system transient stability and method - Google Patents
A kind of optimal corrective control of electric power system transient stability and method Download PDFInfo
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Abstract
A kind of optimal corrective control of electric power system transient stability and method, including data acquisition module, obtain BPA trends form initial data form and BPA transient stability form initial data forms under the current method of operation；Execution module is calculated, BPA power flow files initial data forms and BPA transient stability initial data forms are calculated using BPA flow calculation programs and BPA transient stability computation programs；Data resolution module, BPA trends form initial data form and BPA transient stability form initial data forms are parsed using self-defining data interface module；Execution module is corrected, initial data form is optimized using Modern Interior Point Optimization Algorithm, corrected.The present invention can make the establishment of the transient safe and stable method of operation of power network become simple and easy, shorten workflow and formulate the time, mitigate operations staff's working strength and pressure, improve the quality of voltage and security and stability of operation of power networks comprehensively.
Description
Technical Field
The invention relates to the field of transient stability analysis and optimization of a power system, in particular to a transient stability optimal correction control method of the power system based on BPA and transient stability constraint optimal power flow.
Background
In current competitive power market environments, the operation of a power system is often close to its steady limit state. Once a fault or disturbance occurs, a large-scale power failure accident and even system breakdown are often caused. Therefore, the power system cannot operate in the past conservative mode when the operation stability analysis (particularly transient stability analysis) of the power system and the optimal correction are found in the power market environment, and the transient safety of the system cannot be guaranteed under the condition of failure. This requires that the operation planning must optimize the operating conditions under the premise of satisfying the stability, i.e. adding stability constraints, especially transient stability constraints, to the optimal power flow.
Disclosure of Invention
The invention aims to solve the technical problem that aiming at the defect that the existing power system can not lead the evaluated power system to be in the transient stable power grid operation mode under the sudden failure, the invention provides the optimal correction control system and the optimal correction control method for the transient safety and stability of the power system, so as to improve the power grid transient stability of the evaluated power system, lead the power grid to be always in the transient safe and stable power grid operation mode, carry out the power flow optimization calculation on the power grid of the evaluated power system, realize that the power grid of the evaluated power system can obtain the power grid operation mode optimization data required by the transient safe and stable operation of the evaluated power system through a BPA system under the specified operation mode, automatically calculate and verify the power grid operation mode optimization data, and the verification result can be directly used for guiding the establishment of the transient safe and stable operation mode of the evaluated power system, so as to ensure the safe, stable and reliable operation of the power grid.
In order to solve the technical problems, the invention adopts the following technical scheme:
an optimal correction control system for transient stability of a power system comprises a data acquisition module, a calculation execution module, a data analysis module and a correction execution module. The data acquisition module is used for acquiring a BPA trend format original data report and a BPA transient stable format original data report in the current operation mode; the calculation execution module calculates the BPA power flow file original data report and the BPA transient stability original data report by adopting a BPA power flow calculation program and a BPA transient stability calculation program; the data analysis module is used for analyzing the BPA trend format original data report and the BPA transient stable format original data report by using the user-defined data interface module; and the correction execution module optimizes and corrects the original data report by adopting a modern interior point algorithm.
The control method adaptive to the control system comprises the following steps:
giving a BPA trend format original data report and a BPA transient stable format original data report in an operation mode;
carrying out BPA power flow calculation on data in the BPA power flow format original data report by using BPA power system calculation analysis software;
setting a fault line, a fault occurrence time and a fault removal time, and performing BPA transient stability calculation on data in the BPA transient stability original data report by using BPA power system calculation and analysis software;
judging whether transient stability calculation of the BPA is unstable or not through the limit of the relative swing angle of the generator rotor; if the stable region is insufficient and the system is unstable, starting a transient stability constraint optimal power flow correction calculation program;
analyzing a BPA trend format original data report and a BPA transient stability format original data report containing the network structure and the operation data of the evaluated power system by using a custom data interface module;
starting a transient stability constraint optimal power flow correction calculation program, correcting and setting control variables or constraint conditions of the evaluated power system, and analyzing and solving the corrected and set evaluated power system by adopting an optimal power flow model and an optimal power flow algorithm, wherein the control variables comprise generator active power, generator reactive power and PV node voltage, and the constraint conditions comprise interconnection line constraint and node voltage constraint;
step seven, writing the corrected and set data back to the BPA trend format original data report;
step eight, outputting a BPA flow format optimized data report and a BPA transient stable format optimized data report which enable calculation convergence;
and step nine, covering the data in the BPA flow format original data report with the data in the BPA flow format optimized data report, namely ensuring that the evaluated power system is in a transient safe and stable operation mode, wherein the power grid operation mode is the transient safe and stable operation limit of the evaluated power system.
Preferably, in the fifth step, BPA network node analysis is performed on the network configuration and operation data including the power system under evaluation, and BPA network node equivalent processing is also performed on the network configuration and operation data including the power system under evaluation.
Preferably, in step six, the constraint condition further includes a system power flow constraint for ensuring that the evaluated power system always satisfies the system power flow constraint.
Preferably, in step six, the constraint condition further comprises a generator rotor relative swing angle limit constraint for ensuring that the generator is not unstable in synchronous operation.
Preferably, in the seventh step, if the BPA transient stability calculation is unstable, the original data report is corrected by using the optimal power flow model containing the transient stability constraint, and the data after the correction setting is written back to the BPA power flow format original data report.
According to the scheme, whether a current stabilizing system can be kept stable after experiencing the fault is judged by presetting a system fault, if the system is unstable, the control variable or constraint condition of the evaluated power system is optimized, the unit active power output, the unit reactive power output and the PV node voltage of the evaluated power system are coordinately controlled, an optimized operation configuration strategy for transient state safe and stable operation of the evaluated power system is provided, the transient state safe and stable operation level of the evaluated power system is further improved, and the safe, stable and reliable operation of a power grid of the evaluated power system is ensured. Compared with the prior art, the invention has the following beneficial effects:
1. the method can improve that the power grid of the evaluated power system is always in the transient state safe and stable power grid operation mode, and can perform power flow limit optimization calculation on the power grid of the evaluated power system, so that the power grid of the evaluated power system can obtain power grid operation mode optimization data required by the transient state safe and stable operation of the evaluated power system through a transient state stability constraint optimal power flow correction calculation program in any operation mode, and can perform automatic calculation and verification by using the power grid operation mode optimization data, and the verification result can be directly used for guiding and compiling the power grid operation mode of the transient state safe and stable of the evaluated power system so as to ensure the safe, stable and reliable operation of the power grid.
2. The method can make the establishment of the transient safe and stable operation mode of the power grid simple and easy, shorten the working process and the formulation time, reduce the working intensity and pressure of operators, and comprehensively improve the voltage quality and the safety and stability of the operation of the power grid.
Drawings
Fig. 1 is a block diagram of a transient stability optimal correction control system for an electric power system according to the present invention.
Fig. 2 is a schematic block diagram of a flow of the transient stability optimal correction control method of the power system according to the present invention.
FIG. 3 is a plot of rotor relative yaw before correction of the fault lines FUS 1M-FUS 2M in an exemplary embodiment.
FIG. 4 is a corrected rotor yaw relative curve for the exemplary embodiment of the fault lines FUS 1M-FUS 2M.
FIG. 5 is a rotor yaw relative curve of the embodiment before correction of fault line WENL 2M-LONGB 1M.
FIG. 6 is a corrected rotor yaw relative curve for the embodiment with fault line WENL 2M-LONGB 1M.
FIG. 7 is a rotor yaw curve of the fault line YUZ 1M-YUZ 2M before correction in an exemplary embodiment.
FIG. 8 is a corrected rotor yaw relative curve for fault line YUZ 1M-YUZ 2M in an exemplary embodiment.
FIG. 9 is a rotor yaw curve of the fault line DONGF 2M-LONGB 1M before calibration in an exemplary embodiment.
FIG. 10 is a corrected rotor yaw relative curve for the fault line DONGF 2M-LONGB 1M in an exemplary embodiment.
Fig. 11 is a rotor relative rocking curve of the fault line LUOD2M — length 2M before correction in the exemplary embodiment.
Fig. 12 is a corrected rotor relative rocking curve for the fault line LUOD 2M-long b2M in an example embodiment.
Detailed Description
The technical solution and the advantages of the present invention will be further explained with reference to the following embodiments and the accompanying drawings.
The model is roughly divided into two types, one is based on time domain simulation, a rotor motion equation is converted into an equivalent algebraic equation, and the algebraic equation and an angle criterion are used as constraints and are directly added into the optimal power flow model; or based on the Lyapunov direct method, the equation and the stability criterion are directly added. The former method has accurate model and accurate and reliable result, but has larger calculation amount and longer time consumption; while the latter results are somewhat conservative.
On the basis of the optimal power flow, the differential of the motion equation of the rotor of the generator under the fault is used as equality constraint by using an implicit trapezoidal integral rule, and the limit of the relative swing angle of the rotor is used as inequality constraint and added into the optimal power flow, so that an optimal power flow model of transient stability constraint is established. The objective is to solve an initial system state that exhibits transient stability in the event of a fault, while also meeting economic requirements. The optimal power flow of transient stability constraint belongs to a typical dynamic optimization problem, is also a research hotspot of an electric power system, and is solved by adopting a modern interior point algorithm.
The terms to which the invention relates are to be interpreted as follows:
BPA: the method refers to a power system calculation analysis software package introduced and developed by the Chinese institute of electrical science.
And (3) load flow calculation: the method is characterized in that under a certain operation mode and a certain wiring mode, the voltage, the current and the direction of the power system from a power supply to various places of a load and the distribution situation of the power are calculated.
Transient stability calculation: the method is used for calculating whether the power system can reach a new steady-state operation state or recover to an original state through a transient process after the power system is suddenly subjected to large interference under a certain operation condition. The large disturbance generally means a short-circuit fault, a sudden disconnection of a line, a generator, or the like.
Optimal power flow with transient stability constraints: when the structural parameters and the load condition of the system are given, the available control variables are adjusted, and transient stability constraint conditions are added to find the load flow distribution which can meet all the operation constraint conditions and enable a certain performance index of the system to reach the optimal value.
The mathematical model used in the invention is as follows:
1. objective function
Taking the minimum active power output correction quantity of the generator as an objective function:
wherein, PG1iFor the current generator i active power, PGiTo adjust the active power of the rear generator i.
2. Equality constraint
1) Node injection power flow balance equation
Wherein,
n: the number of nodes;
PDi: the active power of load i;
QRi: reactive power of a reactive power source i;
QDi: the reactive power of the load is;
ei,fi: the real part and the imaginary part of the voltage of the node i;
ej,fj: the voltage amplitude and phase angle of node j;
Gij,Bij: the node admittance real part and the imaginary part of the branch ij;
Sn: a system node set;
2) equation of motion of generator rotor
Differentiating the rotor motion equation by using an implicit trapezoidal integration method to obtain a rotor equation under an expected fault:
wherein,
k: predicting the number of faults;
t: a time period;
ωN: synchronizing the rotating speed;
Δ t: numerical integration step length;
Di: generator i damping coefficient;
the rotation angle of the generator i at each time interval after the fault is removed;
the speed of the generator i at each time interval after the fault is removed;
the electromagnetic power of the generator i at each time interval after the fault is removed;
Ei: the potential amplitude of the generator i;
Ej: the magnitude of the potential of generator j;
Gij: only the real part of the existing admittance array of the generator node is contained after the fault;
Bij: only containing the virtual part of the existing admittance array of the generator node after the fault;
St: a set of time periods.
3) Initial value equation of generator
In steady state operation, the generator potential satisfies the formula:
namely:
wherein,
Ei: the potential amplitude of the generator i;
QGi: reactive power of generator i;
X′d: transient reactance of the generator;
ei，fi: the real part and the imaginary part of the end voltage of the generator i;
and (5) issuing the angle of the generator i in an initial state.
3. Inequality constraint condition
1) Operating constraints
Wherein,
the upper limit of the active power of the generator i;
the active power lower limit of the generator i;
the upper limit of the reactive power source i;
the lower reactive power limit of the reactive power source i;
the upper voltage limit of node i;
the lower voltage limit of node i;
SR: a reactive power supply set;
Sn: a system node set;
2) transient stability constraint
Taking the inertia center COI of the system as a reference, the relative swing angle limit of each generator rotor is as follows:
wherein,
issuing a generator inertia center angle in an initial state;
predicting the inertia center angle of each time interval after the fault is removed;
Mj: the inertia time constant of the jth generator;
a lower limit of the generator rotor angle;
and (4) upper limit of the angle of the generator rotor.
Referring to fig. 1 and 2, the present embodiment is implemented according to the following specific method: setting an expected system fault, a fault occurrence time and a fault removal time in the current stable state of the system through a power system network structure and a load flow format original data report and a transient stability original data report of operation data, and performing BPA load flow calculation and transient stability calculation on data in the original data report; if oscillation occurs in BPA transient stability calculation, correcting and setting control variables or constraint conditions by using a transient stability constraint optimal power flow correction calculation program, and writing corrected data back to a BPA power flow format original data report; outputting a BPA flow format optimized data report and a BPA transient stable format optimized data report when the calculation is converged; and covering the data in the BPA flow format original data report with the data in the BPA flow format optimized data report, so that the evaluated power system can be ensured to be in a transient safe and stable operation mode, wherein the power grid operation mode is the transient safe and stable operation limit of the evaluated power system.
Now, by comprehensively testing a 195-node system of a power grid in a certain area, the minimum active power output correction quantity of the generator after a three-phase short-circuit fault occurs in the middle section of a line of 141 lines is obtained, and a test result of 5 representative lines is given. The analysis steps are as follows:
1. the evaluated power system comprises 195 nodes, 141 lines and 29 generators, and BPA load flow calculation is carried out;
2. setting an expected system fault, and performing BPA transient stability calculation;
3. and if the transient stability calculation cannot be kept stable, performing transient stability constraint optimal power flow optimal correction, and simultaneously setting equivalent control variables and constraint conditions for joint optimization, wherein the algorithm of the joint optimization adopts a modern interior point algorithm.
4. When the power flow calculation is converged and the transient stability calculation is stable, outputting a BPA power flow format optimization data report and a BPA transient stability format optimization data report when the calculation is converged;
5. and covering the data in the BPA flow format original data report with the data in the BPA flow format optimized data report, so that the evaluated power system can be ensured to be in a transient safe and stable operation mode, the power grid operation mode is an optimal transient safe and stable operation mode of the evaluated power system, and a calculation analysis report is output.
In the transient safe and stable operation optimization of the actual power system, the method has very obvious effect on the transient safe and stable operation of the evaluated power system. The following is illustrated by way of example:
2. test result with minimum active output correction of generator as objective function
To show the characteristics of the algorithm, the integral step length is selected to be 0.02s, the minimum generator active output correction is calculated according to the objective function of the minimum generator active output correction, and the method is described in detail through the test results of 5 representative lines. Table 1 is a table of test data with integration step size of 0.02 s.
Table 1195 node system 5 representative line targets are the reference capacity of the test data table with minimum generator active correction: 100MVA
The test result curves are shown in fig. 3-12, wherein fig. 3 and 4 are the relative swing curves of the rotor before and after the calibration of the fault lines FUS 1M-FUS 2M, respectively; FIGS. 5 and 6 are the rotor yaw curves before and after correction of fault line WENL 2M-LONGB 1M, respectively; FIGS. 7 and 8 are graphs of rotor yaw before and after calibration for fault lines YUZ 1M-YUZ 2M, respectively; FIGS. 9 and 10 are the rotor relative rocking curves before and after calibration of the fault line DONGF 2M-LONGB 1M, respectively; fig. 11 and 12 are rotor relative rocking curves before and after correction of the fault line LUOD 2M-LONGB 2M, respectively.
And (3) calculating a curve before correction by transient stability, keeping the current operation state of the system, generating an expected fault at 0s, and cutting off the fault at 0.15s to obtain a simulation curve. And the corrected curve is obtained by calculating an objective function taking the active power output correction quantity of the generator as the minimum. The system changes the current operation state, an expected fault occurs at 0s, and the fault is removed in 0.15 s.
As can be seen from the results of table 1 and fig. 3 to 12, the optimal power flow calculation module with transient stability constraint can effectively perform preventive control on the system. The active output of the generator set is reasonably adjusted; the control of each line of the evaluated power system can meet the safety and stability guide rule of the power system and the voltage quality and reactive power management regulation of the power system. Transient stability of the evaluated power system is effectively controlled.
The embodiments of the present invention have been described above with reference to the accompanying drawings, but the implementation is not limited to the above-described embodiments, and those skilled in the art can make various changes or modifications within the scope of the appended claims.
Claims (1)
1. A control method adaptive to a transient stability optimal correction control system of a power system is characterized in that the transient stability optimal correction control system of the power system comprises a data acquisition module, a calculation execution module, a data analysis module and a correction execution module; the data acquisition module is used for acquiring a BPA trend format original data report and a BPA transient stable format original data report in the current operation mode; the calculation execution module is used for calculating the BPA power flow file original data report and the BPA transient stability original data report by adopting a BPA power flow calculation program and a BPA transient stability calculation program; the data analysis module is used for analyzing the BPA trend format original data report and the BPA transient stable format original data report by using the user-defined data interface module; the correction execution module optimizes and corrects the original data report by adopting a modern interior point algorithm;
the control method comprises the following steps:
giving a BPA trend format original data report and a BPA transient stable format original data report in an operation mode;
carrying out BPA power flow calculation on data in the BPA power flow format original data report by using BPA power system calculation analysis software;
setting a fault line, a fault occurrence time and a fault removal time, and performing BPA transient stability calculation on data in the BPA transient stability original data report by using BPA power system calculation and analysis software;
judging whether transient stability calculation of the BPA is unstable or not through the limit of the relative swing angle of the generator rotor; when the stable region is insufficient and the system is unstable, starting a transient stability constraint optimal power flow correction calculation program;
analyzing a BPA trend format original data report and a BPA transient stability format original data report containing the network structure and the operation data of the evaluated power system by using a custom data interface module; carrying out BPA network node analysis on the network structure and the operation data containing the evaluated power system, and carrying out BPA network node equivalent processing on the network structure and the operation data containing the evaluated power system;
starting a transient stability constraint optimal power flow correction calculation program, correcting and setting control variables or constraint conditions of the evaluated power system, and analyzing and solving the corrected and set evaluated power system by adopting an optimal power flow model and an optimal power flow algorithm, wherein the control variables comprise generator active power, generator reactive power and PV node voltage, and the constraint conditions comprise interconnection line constraint, node voltage constraint, system power flow constraint and motor rotor relative swing angle limit constraint;
step seven, writing the corrected and set data back to the BPA trend format original data report; when the BPA transient stability calculation is unstable, correcting the original data report by adopting an optimal power flow model containing transient stability constraint, and writing back the data after correction setting to the BPA power flow format original data report;
step eight, outputting a BPA flow format optimized data report and a BPA transient stable format optimized data report when calculation convergence occurs;
step nine, covering the data in the BPA flow format original data report with the data in the BPA flow format optimized data report, namely ensuring that the evaluated power system is in a transient safe and stable operation mode, wherein the transient safe and stable operation mode is the transient safe and stable operation limit of the evaluated power system;
the optimal power flow model comprises:
(one) objective function: taking the minimum active power output correction of the generator as a target function;
<mrow> <mi>min</mi> <mi> </mi> <mi>f</mi> <mrow> <mo>(</mo> <mo>&CenterDot;</mo> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>&Element;</mo> <msub> <mi>S</mi> <mi>G</mi> </msub> </mrow> </munder> <msup> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>G</mi> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>G</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>;</mo> </mrow>
wherein, PG1iFor the current generator i active power, PGiThe active power of the generator i is adjusted;
(II) equation constraint conditions:
1) node injection power flow balance equation:
wherein n is the number of nodes; pDiIs the active power of load i; qRiIs the reactive power of the reactive power source i; qDiIs the reactive power of the load; e.g. of the typei,fiThe real part and the imaginary part of the voltage of the node i; e.g. of the typej,fjIs the voltage amplitude and phase angle of node j; gij,BijThe real part and the imaginary part of the node admittance of the branch ij; snIs a system node set;
2) generator rotor equation of motion:
differentiating the rotor motion equation by using an implicit trapezoidal integration method to obtain a rotor equation under an expected fault:
wherein,k is the expected failure number; t is a time period; omegaNThe synchronous rotating speed is adopted; Δ t is a numerical integration step; diThe damping coefficient of the generator i;turning angles of the generator i at each time interval after fault removal;the speed of the generator i in each time interval after the fault is removed;the electromagnetic power of the generator i at each time interval after the fault is removed; eiIs the potential amplitude of the generator i; ejIs the potential amplitude of generator j; gijThe real part of the existing admittance array only containing the generator node after the fault; b isijThe imaginary part of the existing admittance array only containing the generator node after the fault; stIs a set of time periods;
3) generator initial value equation:
in steady state operation, the generator potential satisfies the formula:
<mrow> <msub> <mi>E</mi> <mi>i</mi> </msub> <mo>&angle;</mo> <msubsup> <mi>&delta;</mi> <mi>i</mi> <mn>0</mn> </msubsup> <mo>=</mo> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>i</mi> </msub> <mo>+</mo> <mi>j</mi> <mfrac> <mrow> <msub> <mi>P</mi> <mrow> <mi>G</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>jQ</mi> <mrow> <mi>G</mi> <mi>i</mi> </mrow> </msub> </mrow> <msub> <mover> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mo>^</mo> </mover> <mi>i</mi> </msub> </mfrac> <msubsup> <mi>X</mi> <mrow> <mi>d</mi> <mi>i</mi> </mrow> <mo>&prime;</mo> </msubsup> </mrow>
namely:
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <mi>i</mi> </msub> <msub> <mi>e</mi> <mi>i</mi> </msub> <msubsup> <mi>sin&delta;</mi> <mi>i</mi> <mn>0</mn> </msubsup> <mo>-</mo> <msub> <mi>E</mi> <mi>i</mi> </msub> <msub> <mi>f</mi> <mi>i</mi> </msub> <msubsup> <mi>cos&delta;</mi> <mi>i</mi> <mn>0</mn> </msubsup> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>G</mi> <mi>i</mi> </mrow> </msub> <msubsup> <mi>X</mi> <mrow> <mi>d</mi> <mi>i</mi> </mrow> <mo>&prime;</mo> </msubsup> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>e</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>f</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msub> <mi>E</mi> <mi>i</mi> </msub> <msub> <mi>e</mi> <mi>i</mi> </msub> <msubsup> <mi>cos&delta;</mi> <mi>i</mi> <mn>0</mn> </msubsup> <mo>-</mo> <msub> <mi>E</mi> <mi>i</mi> </msub> <msub> <mi>f</mi> <mi>i</mi> </msub> <msubsup> <mi>sin&delta;</mi> <mi>i</mi> <mn>0</mn> </msubsup> <mo>+</mo> <msub> <mi>Q</mi> <mrow> <mi>G</mi> <mi>i</mi> </mrow> </msub> <msubsup> <mi>X</mi> <mrow> <mi>d</mi> <mi>i</mi> </mrow> <mo>&prime;</mo> </msubsup> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced>
wherein E isiIs the potential amplitude of the generator i; qGiIs the reactive power of generator i; x'dIs a generator transient reactance; e.g. of the typeiAnd fiThe real part and the imaginary part of the end voltage of the generator i are shown;the angle of a generator i is in an initial state;
(III) inequality constraint conditions:
1) and (4) operation constraint:
wherein,the upper limit of the active power of the generator i;P Giis the active power lower limit of generator i;the upper limit of the reactive power source i;Q Riis the lower reactive power limit of the reactive power source i;is the upper voltage limit of node i;V iis the lower voltage limit of node i; sRIs a reactive power supply set; snIs a system node set;
2) transient stability constraint:
taking the inertia center COI of the system as a reference, the relative swing angle limit of each generator rotor is as follows:
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <munder> <mi>&delta;</mi> <mo>&OverBar;</mo> </munder> <mo>&le;</mo> <msubsup> <mi>&delta;</mi> <mi>i</mi> <mn>0</mn> </msubsup> <mo>-</mo> <msubsup> <mi>&delta;</mi> <mrow> <mi>C</mi> <mi>O</mi> <mi>I</mi> </mrow> <mn>0</mn> </msubsup> <mo>&le;</mo> <mover> <mi>&delta;</mi> <mo>&OverBar;</mo> </mover> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munder> <mi>&delta;</mi> <mo>&OverBar;</mo> </munder> <mo>&le;</mo> <msubsup> <mi>&delta;</mi> <mi>i</mi> <mi>t</mi> </msubsup> <mo>-</mo> <msubsup> <mi>&delta;</mi> <mrow> <mi>C</mi> <mi>O</mi> <mi>I</mi> </mrow> <mi>t</mi> </msubsup> <mo>&le;</mo> <mover> <mi>&delta;</mi> <mo>&OverBar;</mo> </mover> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <msub> <mi>S</mi> <mi>G</mi> </msub> <mo>,</mo> <mi>t</mi> <mo>&Element;</mo> <msub> <mi>S</mi> <mi>t</mi> </msub> </mrow>
wherein, generating an inertia center angle of the generator in an initial state;the angle of the inertia center of each time interval after the expected fault is removed; mjIs the inertia time constant of the jth generator; is the lower limit of the angle of the generator rotor;is the upper limit of the angle of the rotor of the generator.
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