CN107968396B - Thevenin equivalent parameter calculation method based on local phasor measurement information - Google Patents
Thevenin equivalent parameter calculation method based on local phasor measurement information Download PDFInfo
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- CN107968396B CN107968396B CN201711184717.6A CN201711184717A CN107968396B CN 107968396 B CN107968396 B CN 107968396B CN 201711184717 A CN201711184717 A CN 201711184717A CN 107968396 B CN107968396 B CN 107968396B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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Abstract
The invention relates to a Thevenin equivalent parameter calculation method based on local phasor measurement information, which comprises the following steps: according to the variation of the Thevenin equivalent parameter, establishing a loop voltage equation of the Thevenin equivalent system; determining the relationship between thevenin equivalent parameters at adjacent moments according to a Taylor formula; and acquiring local phasor measurement information, and solving to obtain thevenin equivalent parameters at the current moment according to the established loop voltage equation and the determined relationship between thevenin equivalent parameters at the adjacent moments. Compared with the prior art, the method has the advantages of avoiding parameter drift and being not interfered by the position where disturbance occurs and the like.
Description
Technical Field
The invention relates to the field of on-line monitoring and control of an electric power system, in particular to a Thevenin equivalent parameter calculation method based on local phasor measurement information.
Background
Thevenin equivalent parameters are widely applied to the aspects of fault location, system instability mode identification, voltage stability margin detection and the like, and meanwhile, accurate calculation of the Thevenin equivalent parameters becomes an important premise for effectively utilizing the Thevenin equivalent parameters.
According to different data sources, the tracking method of thevenin equivalent parameters can be mainly divided into an external measurement method for solving thevenin equivalent parameters according to local measurement values and an internal interpolation method for solving thevenin equivalent parameters according to the internal network topology structure of the system.
The Thevenin equivalent parameters of the system can be solved and obtained by an external measurement method only according to the local phasor measurement value, and the method has the characteristics of quick calculation, small calculation amount and the like. However, the essence of the algorithm is that the Thevenin equivalent parameters are not changed greatly in adjacent moments, so that the tracking accuracy is poor, the applicable environment is single, and the problems that the Thevenin equivalent parameters cannot be solved correctly when disturbance exists in the system, the parameters drift, the initial value of the Thevenin equivalent parameters is solved and the like exist.
The interpolation method utilizes the network topology structure of the system to calculate thevenin equivalent parameters of the system. Because the method does not need any hypothesis and solves the Thevenin equivalent parameters only according to the network structure of the system, the Thevenin equivalent parameters obtained by the algorithm are most accurate, and the size and the position of disturbance in the system can not influence the calculation accuracy of the algorithm. However, such algorithms have high requirements on the arrangement of the measurement devices and the communication devices in the system, and each node in the system needs to be provided with a PUM or other measurement devices.
Disclosure of Invention
The invention aims to provide a Thevenin equivalent parameter calculation method based on local phasor measurement information.
The purpose of the invention can be realized by the following technical scheme:
a Thevenin equivalent parameter calculation method based on local phasor measurement information comprises the following steps:
1) according to the variation of the Thevenin equivalent parameter, establishing a loop voltage equation of the Thevenin equivalent system;
2) determining the relationship between thevenin equivalent parameters at adjacent moments according to a Taylor formula;
3) collecting local phasor measurement information, and solving to obtain thevenin equivalent parameters at the current moment according to the loop voltage equation established in the step 1) and the relation between thevenin equivalent parameters at the adjacent moments determined in the step 2).
Preferably, the loop voltage equation of the thevenin equivalent system is specifically as follows:
where k is the time k, k +1 is the next time of the time k, ImMeasuring the amplitude, V, of the current value for the local phasormMeasuring the amplitude of the voltage value for the local phasor, EmIs the amplitude of thevenin equivalent potential, ZmIs the amplitude of thevenin equivalent impedance,
is the argument of thevenin equivalent potential,
the argument of thevenin equivalent impedance is theta, the phase angle of the current value of the local phasor measurement, and alpha is the phase angle of the voltage value of the local phasor measurement.
Preferably, the relationship between thevenin equivalent parameters at adjacent times is specifically as follows:
wherein the content of the first and second substances,
in order to realize the purpose,
is o (h)2) Is a high order term.
Preferably, the step 3) includes:
31) substituting the relation between thevenin equivalent parameters at the adjacent moments determined in the step 2) into the loop voltage equation established in the step 1) to obtain a thevenin equivalent parameter solution equation set;
32) collecting local phasor measurement information at a specific collection frequency;
33) and (3) substituting the local phasor measurement information acquired in the step 32) into the Thevenin equivalent parameter solving equation set obtained in the step 31) for solving, and calculating to obtain the Thevenin equivalent parameter at the current moment.
Preferably, the Thevenin equivalent parameter solution equation set specifically comprises:
wherein f is1、f2、f3、f4、f5And f6Respectively are six functional relational expressions obtained by substituting the relationship between thevenin equivalent parameters at adjacent moments into a loop voltage equation, wherein k is the moment k, k +1 is the next moment of the moment k, and I ismMeasuring the amplitude, V, of the current value for the local phasormMeasuring the amplitude of the voltage value for the local phasor, EmIs the amplitude of thevenin equivalent potential, ZmIs the amplitude of thevenin equivalent impedance,
is the argument of thevenin equivalent potential,
the argument of thevenin equivalent impedance is theta, the phase angle of the current value of the local phasor measurement, and alpha is the phase angle of the voltage value of the local phasor measurement.
Preferably, the specific acquisition frequency is specifically: greater than the variation frequency of thevenin equivalent system.
Preferably, the local phasor measurement information includes a local phasor measurement voltage value and a local phasor measurement current value.
Compared with the prior art, the invention has the following beneficial effects:
(1) according to the method, the Thevenin equivalent parameters of the system can be calculated by using the Taylor expansion only by using the voltage and current information in the local phasor measurement value, so that the problem of high requirement on measurement equipment in an interpolation method is solved, and the cost is saved. Meanwhile, on the basis of the Taylor expansion, the method provided by the invention weakens the linearization degree of local measurement values at adjacent moments by establishing a loop voltage equation of a Thevenin equivalent system, thereby avoiding the parameter drift problem caused by the linearization degree; meanwhile, tracking of the Thevenin equivalent parameters is converted into tracking of the Thevenin equivalent parameters on the variation of the Thevenin equivalent parameters at the adjacent moment by using the Taylor expansion, so that the Thevenin equivalent parameters can be calculated when disturbance occurs inside or outside the equivalent system, and the problem that the solving result of an external measuring method is inaccurate is solved.
(2) When the local phasor measurement information is acquired, the acquisition frequency needs to be greater than the change frequency of the thevenin equivalent system, because if the sampling frequency is faster in the actual calculation process, the acquisition frequency is higher than the change frequency of the thevenin equivalent system
Furthermore, the first order Taylor expansion can satisfy the solution accuracy, and the high order term o (h2) can be omitted. In a steady-state process with slow system change, the condition of the sampling frequency is easier to meet, meanwhile, the amplitude of thevenin equivalent parameters at the adjacent moment is assumed to be unchanged, 6 equations in an equation set are solved according to the thevenin equivalent parameters, and the thevenin equivalent parameters at the moment can be quickly solved without an initial value solution.
Drawings
FIG. 1 is a flow chart of a method of Thevenin equivalent parameter calculation method based on local phasor measurement information;
FIG. 2 is a schematic structural diagram of a three-machine nine-node system in an embodiment;
FIG. 3 is a simulation result diagram of Thevenin equivalent parameters in the example;
FIG. 4 is a diagram showing simulation results of indirect verification in the embodiment.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
As shown in fig. 1, this embodiment provides a method for calculating thevenin equivalent parameters based on local phasor measurement information, which includes the following steps:
1) according to the variation of thevenin equivalent parameters, a loop voltage equation of the thevenin equivalent system is established, and the loop voltage equation of the thevenin equivalent system specifically comprises the following steps:
where k is the time k, k +1 is the next time of the time k, ImMeasuring the amplitude, V, of the current value for the local phasormMeasuring the amplitude of the voltage value for the local phasor, EmIs the amplitude of thevenin equivalent potential, ZmIs the amplitude of thevenin equivalent impedance,
is the argument of thevenin equivalent potential,
is the argument of thevenin equivalent impedance, theta is the phase angle of the local phasor measurement current value, and alpha is the phase angle of the local phasor measurement voltage value;
2) determining the relationship between thevenin equivalent parameters at adjacent moments according to a Taylor formula, which specifically comprises the following steps:
wherein the content of the first and second substances,
is the argument of thevenin equivalent potential,
is thevenin, etcArgument of value impedance, o (h)2) Is a high-order term;
3) collecting local phasor measurement information, and solving to obtain thevenin equivalent parameters at the current moment according to the loop voltage equation established in the step 1) and the relation between thevenin equivalent parameters at the adjacent moments determined in the step 2), wherein the method comprises the following steps of:
31) substituting the relation between thevenin equivalent parameters at adjacent moments determined in the step 2) into the loop voltage equation established in the step 1) to obtain a thevenin equivalent parameter solution equation set, which specifically comprises the following steps:
wherein f is1、f2、f3、f4、f5And f6Respectively are six functional relational expressions obtained by substituting the relationship between thevenin equivalent parameters at adjacent moments into a loop voltage equation, wherein k is the moment k, k +1 is the next moment of the moment k, and I ismMeasuring the amplitude, V, of the current value for the local phasormMeasuring the amplitude of the voltage value for the local phasor, EmIs the amplitude of thevenin equivalent potential, ZmIs the amplitude of thevenin equivalent impedance,
is the argument of thevenin equivalent potential,
is the argument of thevenin equivalent impedance, theta is the phase angle of the local phasor measurement current value, and alpha is the phase angle of the local phasor measurement voltage value;
32) local phasor measurement information is acquired at a specific acquisition frequency, which specifically comprises: greater than the variation frequency of thevenin equivalent system;
33) and (3) bringing the local phasor measurement information (including the local phasor measurement voltage value and the local phasor measurement current value) acquired in the step 32) into the Thevenin equivalent parameter solving equation set obtained in the step 31), and solving to obtain the Thevenin equivalent parameter at the current moment by calculation.
In this embodiment, according to the above method, specific experimental verification is performed, and the process is as follows:
according to KVL assumption, assuming that only the amplitude of thevenin equivalent parameters does not change at adjacent time, listing a loop voltage equation of the thevenin equivalent system at the adjacent time:
in the formula (I), the compound is shown in the specification,
in the above formula, Δ represents the variation of argument in thevenin equivalent parameter at the adjacent time.
The conventional loop voltage equation is generally:
the loop voltage equation established in the embodiment increases the argument variation of thevenin equivalent parameters, and the parameter drift phenomenon existing in the solving process of thevenin equivalent parameters is avoided in degree by tracking the incremental information of thevenin equivalent parameters.
According to higher mathematical knowledge, the argument of thevenin equivalent parameter at the k +1 th time can be expanded by taylor expansion, as shown in the following formula. For simplicity, the following equations are all expanded to the first order, where o (h)2) Representing the higher order terms in the taylor formula:
the expansion is substituted into the loop voltage equation established by substitution, so that six groups of equations can be obtained
In the above formula, the known amount is
Unknown quantity is
If the sampling frequency is faster in the actual calculation process, then
Furthermore, the first order Taylor expansion can satisfy the solution accuracy, and the high order term o (h2) can be omitted. In the steady-state process that the system changes slowly, the requirement of sampling frequency can become low, so the above condition is easy to meet, and meanwhile, assuming that the amplitude of thevenin equivalent parameters at adjacent moments is unchanged, according to the 6 equations in the above formula, thevenin equivalent parameters at the moment can be quickly solved without initial value solution.
The WCSS three-machine nine-node system with the fan system is adopted for verification, and the topological structure of the exemplary system is shown in figure 2. And designing 0s-10s as internal disturbance and 10s-14s as external disturbance, and respectively simulating the state of only external disturbance and the state of only internal disturbance in the system. The accuracy of the method proposed in this example can be verified using the following formula:
wherein
And the equivalent node bus voltage is calculated by utilizing a Thevenin equivalent parameter group composed of Thevenin equivalent parameters.
And the equivalent node bus voltage obtained by the simulation system through transient simulation calculation is shown. If the equivalent node bus voltage obtained by using Thevenin equivalent parameter calculation is consistent with the equivalent node bus voltage obtained by simulation calculation of the simulation system, the method is proved to be effective.
As shown in FIG. 3, the Load change amount is very small due to Load A within 0-10s, and the duration is very long. Meanwhile, because the disturbance is only applied to the system side in the time period and no disturbance is applied to the Load side, the influence of the change of the Load A on the Load side is very small, and therefore the process in the time period can be used for simulating the state that the Load change of the equivalent point is very stable. When the load change of the equivalent point is very stable, the sampling frequency is high, and the change of the electrical quantity between adjacent moments is small, so that the coefficient matrix tends to be singular in the process of solving thevenin equivalent parameters by the traditional method, namely the phenomenon of parameter drift. In fig. 3, in 0-10s, the fluctuation of the traditional method is very severe in 0-10s, that is, a parameter drift phenomenon occurs, and thevenin equivalent parameters cannot be obtained by correct solution. Correspondingly, the Thevenin equivalent parameters can be obtained by solving the method within 0-10s, and although the algorithm has certain fluctuation within the first few seconds of simulation, the algorithm tends to be stable after a short time.
As shown in fig. 3, after 10s, the disturbance in the system is shifted to the load side, the assumption of the conventional method is satisfied, and both the conventional method and the method proposed in this embodiment can calculate thevenin equivalent parameters, and the calculated values of both methods are substantially the same. Due to the fact that the load increasing state changes violently, the two methods fluctuate greatly within about 10s, but both tend to be in a stable state within a short time.
In addition, because the load disturbance is small in the simulation process, the structure of the system is not changed greatly, so that thevenin equivalent parameters of the system cannot be changed greatly. Meanwhile, in the traditional method, under the condition that only the load side is disturbed, the Thevenin equivalent parameter obtained by calculation is more accurate. When the system disturbance is transferred from the system side to the load side, the Thevenin equivalent impedance obtained by the method provided by the embodiment tends to be stable after short oscillation, and is basically consistent with the Thevenin equivalent parameter value obtained by the traditional method when only the load side is disturbed, so that the correctness of the method provided by the embodiment is proved on the side surface.
Then, the method provided by the embodiment is indirectly verified by using the verification formula, and the simulation result of the indirect verification is shown in fig. 4. The calculated voltage in the diagram is Bus 6 Bus voltage calculated by the Thevenin equivalent parameters calculated by the method provided by the embodiment according to a verification formula, and the calculated value is Bus 6 Bus voltage simulation value calculated by the transient state of simulation software. As can be obtained from fig. 4, the calculated value of the Bus voltage of Bus 6 is very close to the simulation value, and the error between the Bus 6 voltage calculated by the method provided in this embodiment and the simulation value is only 1.3% on the basis of the simulation value, which proves that the provided thevenin equivalent parameter can be calculated more accurately.
Claims (3)
1. A Thevenin equivalent parameter calculation method based on local phasor measurement information is characterized by comprising the following steps:
1) according to the variation of thevenin equivalent parameters, a loop voltage equation of the thevenin equivalent system is established,
2) determining the relationship between thevenin equivalent parameters at adjacent moments according to a Taylor formula,
3) collecting local phasor measurement information, and solving to obtain thevenin equivalent parameters at the current moment according to the loop voltage equation established in the step 1) and the relation between thevenin equivalent parameters at the adjacent moments determined in the step 2);
the loop voltage equation of the Thevenin equivalent system is specifically as follows:
where k is the time k, k +1 is the next time of the time k, ImMeasuring the amplitude, V, of the current value for the local phasormMeasuring the amplitude of the voltage value for the local phasor, EmIs the amplitude of thevenin equivalent potential, ZmIs the amplitude of thevenin equivalent impedance,
is the argument of thevenin equivalent potential,
is the argument of thevenin equivalent impedance, theta is the phase angle of the local phasor measurement current value, and alpha is the phase angle of the local phasor measurement voltage value;
the relationship between thevenin equivalent parameters at adjacent moments is specifically as follows:
wherein, o (h)2) Is a high-order term;
the step 3) comprises the following steps:
31) substituting the relation between thevenin equivalent parameters at the adjacent moments determined in the step 2) into the loop voltage equation established in the step 1) to obtain a thevenin equivalent parameter solution equation set,
32) collecting local phasor measurement information at a specific collection frequency, wherein the specific collection frequency is specifically as follows: greater than the variation frequency of thevenin equivalent system,
33) and (3) substituting the local phasor measurement information acquired in the step 32) into the Thevenin equivalent parameter solving equation set obtained in the step 31) for solving, and calculating to obtain the Thevenin equivalent parameter at the current moment.
2. The Thevenin equivalent parameter calculation method based on local phasor measurement information according to claim 1, wherein the Thevenin equivalent parameter solution equation set specifically comprises:
wherein f is1、f2、f3、f4、f5And f6Respectively are six functional relational expressions obtained by substituting the relationship between thevenin equivalent parameters at adjacent moments into a loop voltage equation, wherein k is the moment k, k +1 is the next moment of the moment k, and I ismMeasuring the amplitude, V, of the current value for the local phasormMeasuring the amplitude of the voltage value for the local phasor, EmIs the amplitude of thevenin equivalent potential, ZmIs the amplitude of thevenin equivalent impedance,
is the argument of thevenin equivalent potential,
the argument of thevenin equivalent impedance is theta, the phase angle of the current value of the local phasor measurement, and alpha is the phase angle of the voltage value of the local phasor measurement.
3. The Thevenin equivalent parameter calculation method based on local phasor measurement information according to claim 1, wherein the local phasor measurement information comprises a local phasor measurement voltage value and a local phasor measurement current value.
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| CN101350524A (en) * | 2008-09-11 | 2009-01-21 | 中国电力科学研究院 | Computation method capable of tracking Davinan equivalence parameter base on total differential equation |
| CN104701851A (en) * | 2015-03-06 | 2015-06-10 | 东南大学 | Partitioned load switching cooperative method for maintaining voltage stabilization of electric system |
| CN105958483A (en) * | 2016-05-31 | 2016-09-21 | 华南理工大学 | Resident distribution unit area three phase unbalanced load flow calculating method taking regard of load characteristics |
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