WO2023124592A1 - 基于逆黑盒及逆电磁对偶模型的pt一次电压重构方法 - Google Patents
基于逆黑盒及逆电磁对偶模型的pt一次电压重构方法 Download PDFInfo
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- the invention relates to the field of measurement technology, in particular to a PT primary voltage reconstruction method, device and equipment based on an inverse black box and an inverse electromagnetic dual model.
- Voltage measurement and its on-line monitoring are key to reliable operation of metering, fault diagnosis and fault protection in power systems.
- the measured voltage waveform is one of the most informative and convincing waveforms in the power system.
- the voltage of the voltage system is often measured by an electromagnetic voltage transformer (Potential transformer, PT).
- PT is a kind of instrument transformer.
- the primary winding of PT is directly connected to the power grid, and the secondary winding of PT is connected to the metering instrument.
- voltage-related fault diagnosis and fault protection depend on the accurate voltage signal output by the secondary side of the PT.
- the PT When the PT works within its rated frequency (50/60Hz) and rated voltage range, it can provide accurate and stable measurement results, its voltage transfer characteristics are constant, there is almost no phase difference between the primary voltage and the secondary voltage, and the ratio of the amplitude is the turns ratio.
- the PT primary side primary winding
- the PT’s secondary-side signal may be distorted, showing a significant difference from the original primary-side voltage, which means that the PT Transient voltage measurements provided under voltage excitation are very inaccurate. Distorted PT secondary signals cause potential hidden dangers to fault diagnosis and protection operations based on voltage signals. At the same time, the distorted voltage signal will seriously mislead the analysis and recovery after the accident.
- the embodiment of the present invention provides a PT primary voltage reconstruction method, device and equipment based on the inverse black box and inverse electromagnetic dual model, which is used to solve the problem that the existing power system uses PT to measure voltage, and the PT has distortion during the measurement process. Technical problems that lead to inaccurate measurement data.
- a PT primary voltage reconstruction method based on an inverse black box and an inverse electromagnetic dual model comprising the following steps:
- the high-frequency voltage component of the primary voltage and the low-frequency voltage component of the primary voltage are integrated to obtain the primary voltage of the power system.
- dividing the secondary voltage signal into low-frequency voltage components and high-frequency voltage components includes:
- the secondary voltage signal is processed by Fourier transform to obtain the frequency domain form of the secondary voltage signal
- Whether the frequency in the frequency domain form of the secondary voltage signal is greater than the transition frequency is divided into a secondary voltage signal low frequency frequency domain and a secondary voltage signal high frequency frequency domain;
- Inverse Fourier transform is applied to the low-frequency domain of the secondary voltage signal and the high-frequency domain of the secondary voltage signal, respectively, to obtain corresponding low-frequency voltage components and high-frequency voltage components.
- the step of reconstructing the primary voltage using an inverse black-box model for the high-frequency voltage component, and obtaining the high-frequency voltage component of the primary voltage includes:
- the high-frequency voltage component is used as the input of the inverse black-box model, and the high-frequency voltage component is reconstructed and transformed through the transfer function of the inverse black-box model, and the inverse black-box model outputs the primary voltage high-frequency voltage component;
- the output variable of the black-box model, H m -1 (s) is the transfer function of the inverse black-box model.
- reconstructing and transforming the high-frequency voltage component through the transfer function of the inverse black-box model includes:
- the discrete voltage reconstruction function is:
- x is the reference variable symbol
- k and k-1 are the time points of the kth and k-1th high-frequency voltage components respectively
- A is the N ⁇ N diagonal matrix of transfer function poles
- B is N ⁇ N 1 array
- ⁇ t is the time interval between the kth high-frequency voltage component and the k-1th high-frequency voltage component
- C is a 1 ⁇ N array of zero points of the transfer function
- D is a constant term.
- the inverse electromagnetic dual model is used to reconstruct the primary voltage for the low-frequency voltage component, and the step of obtaining the low-frequency voltage component of the primary voltage includes:
- the low-frequency voltage component is used as the input of the inverse electromagnetic dual model, and the low-frequency voltage component is reconstructed and transformed through the flux linkage conservation of the inverse electromagnetic dual model and Kirchhoff's current-voltage law, and the inverse electromagnetic dual model outputs the primary voltage low-frequency voltage component;
- v pl nv m1 + R s1 i pl ;
- v m1 v Ls +v m2 ;
- v pl is the low-frequency voltage component of the primary voltage
- n is the turns ratio of the inverse electromagnetic dual model
- v m1 is the voltage of the first excitation branch in the inverse electromagnetic dual model
- v m2 is the second excitation in the inverse electromagnetic dual model
- the voltage of the branch v Ls is the voltage at both ends of the leakage inductance in the inverse electromagnetic dual model
- R s1 is the resistance of the primary winding in the inverse electromagnetic dual model
- i pl is the primary current of the inverse electromagnetic dual model
- i m1 is the inverse electromagnetic dual model
- i Ls is the current flowing through both ends of the leakage inductance in the inverse electromagnetic dual model.
- the PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model includes: adding and integrating the high-frequency voltage component of the primary voltage and the low-frequency voltage component of the primary voltage to obtain the primary voltage of the power system.
- the present invention also provides a PT primary voltage reconstruction device based on an inverse black box and an inverse electromagnetic dual model, including: a frequency component extraction module, a high-frequency inverse calculation module, a low-frequency inverse calculation module, and an integration module;
- the frequency component extraction module is used to collect the secondary voltage signal of the power system through the PT, and divide the secondary voltage signal into a low-frequency voltage component and a high-frequency voltage component;
- the high-frequency inverse calculation module is used to reconstruct the primary voltage of the high-frequency voltage component using an inverse black-box model to obtain a high-frequency voltage component of the primary voltage;
- the low-frequency inverse calculation module is used to reconstruct the primary voltage of the low-frequency voltage component using an inverse electromagnetic dual model to obtain a low-frequency voltage component of the primary voltage;
- the integration module is used to integrate the high-frequency voltage component of the primary voltage and the low-frequency voltage component of the primary voltage to obtain the primary voltage of the power system.
- the high-frequency inverse calculation module is also used to use the high-frequency voltage component as the input of the inverse black-box model, and perform reconstruction transformation on the high-frequency voltage component through the transfer function of the inverse black-box model, and the inverse black-box model
- the box model outputs the primary voltage high-frequency voltage component
- v ph (s) H m -1 (s)v sh (s), where v sh (s) is the input variable of the inverse black box model, and v ph (s) is the inverse black box Model output variable, H m -1 (s) is the transfer function of the inverse black box model;
- the high-frequency inverse calculation module includes a conversion sub-module and a calculation sub-module
- the conversion sub-module is used to perform fitting conversion on the transfer function to obtain a state equation of the transfer function; and introduce a variable x and a central difference method to convert the state equation to obtain a discrete voltage reconstruction function;
- the calculation sub-module is used to iteratively calculate the discrete voltage reconstruction function to obtain a reconstructed high-frequency voltage component of the primary voltage
- the discrete voltage reconstruction function is:
- x is the reference variable symbol
- k and k-1 are the time points of the kth and k-1th high-frequency voltage components respectively
- A is the N ⁇ N diagonal matrix of transfer function poles
- B is N ⁇ N 1 array
- ⁇ t is the time interval between the kth high-frequency voltage component and the k-1th high-frequency voltage component
- C is a 1 ⁇ N array of zero points of the transfer function
- D is a constant term.
- the low-frequency inverse calculation module is also used to use the low-frequency voltage component as the input of the inverse electromagnetic dual model, and conduct the low-frequency voltage component through the flux linkage conservation of the inverse electromagnetic dual model and Kirchhoff's current-voltage law. Reconstruction transformation, the inverse electromagnetic dual model outputs the low-frequency voltage component of the primary voltage:
- v pl nv m1 + R s1 i pl ;
- v m1 v Ls +v m2 ;
- v pl is the low-frequency voltage component of the primary voltage
- n is the turns ratio of the inverse electromagnetic dual model
- v m1 is the voltage of the first excitation branch in the inverse electromagnetic dual model
- v m2 is the second excitation in the inverse electromagnetic dual model
- the voltage of the branch v Ls is the voltage at both ends of the leakage inductance in the inverse electromagnetic dual model
- R s1 is the resistance of the primary winding in the inverse electromagnetic dual model
- i pl is the primary current of the inverse electromagnetic dual model
- i m1 is the inverse electromagnetic dual model
- i Ls is the current flowing through both ends of the leakage inductance in the inverse electromagnetic dual model.
- the present invention also provides a PT primary voltage reconstruction device based on an inverse black box and an inverse electromagnetic dual model, including a processor and a memory;
- the memory is used to store program codes and transmit the program codes to the processor
- the processor is configured to execute the above-mentioned PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model according to the instructions in the program code.
- the embodiment of the present invention has the following advantages: the PT primary voltage reconstruction method, device and equipment based on the inverse black box and inverse electromagnetic dual model, the steps of the method include: collecting the secondary data of the power system through the PT Secondary voltage signal, and divide the secondary voltage signal into low-frequency voltage component and high-frequency voltage component; for high-frequency voltage component, use the inverse black box model to reconstruct the primary voltage, and obtain the primary voltage high-frequency voltage component; for low-frequency voltage component, use The inverse electromagnetic dual model reconstructs the primary voltage to obtain the low-frequency voltage component of the primary voltage; integrates the high-frequency voltage component of the primary voltage and the low-frequency voltage component of the primary voltage to obtain the primary voltage of the power system.
- the PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model uses the inverse black box model and the inverse electromagnetic dual model to process the high-frequency voltage component and low-frequency voltage component divided by the secondary voltage signal collected by the PT respectively, and obtains a primary
- the high-frequency voltage component of the voltage and the low-frequency voltage component of the primary voltage are added to obtain the primary voltage.
- the obtained primary voltage is not affected by the distortion in the PT acquisition process, and the data accuracy is high; it solves the problem of using PT to measure voltage in the existing power system. During the measurement process, PT is distorted, which leads to technical problems of inaccurate measurement data.
- Fig. 1 is a flow chart of the steps of the PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model described in the embodiment of the present invention
- Fig. 2 is a flow chart of the steps of signal division of the PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model described in the embodiment of the present invention
- FIG. 3 is a schematic diagram of the inverse electromagnetic dual model of the PT primary voltage reconstruction method based on the inverse black box and the inverse electromagnetic dual model described in the embodiment of the present invention
- Fig. 4 is a comparison diagram of the PT primary voltage reconstruction method and the distorted signal based on the inverse black box and inverse electromagnetic dual model described in the embodiment of the present invention
- Fig. 5 is a comparison diagram of a PT primary voltage reconstruction method based on an inverse black box and an inverse electromagnetic dual model and a distorted signal according to another embodiment of the present invention
- Fig. 6 is a frame diagram of a PT primary voltage reconstruction device based on an inverse black box and an inverse electromagnetic dual model according to an embodiment of the present invention.
- Electromagnetic voltage transformer is a voltage measurement device that realizes electromagnetic isolation through a transformer, and is also an instrument transformer, the basic principle of which is exactly the same as that of a transformer.
- On-line monitoring refers to the continuous or regular monitoring of the status of the equipment under the condition that the equipment under test is running, usually automatically.
- the PT primary side refers to the PT primary side winding (high voltage winding) directly connected to the power grid.
- the PT primary voltage refers to the voltage across the PT primary winding.
- the PT secondary side refers to the direct connection between the PT secondary winding (low voltage winding) and the metering device.
- the PT secondary signal refers to the voltage across the PT secondary winding, which is also the signal to be measured.
- the black box model refers to a port equivalent model, which has no physical meaning and can only realize the consistency of the port characteristics with the modeled device.
- PT's black box model has remarkable accuracy in simulating high-frequency characteristics, but due to measurement and other factors in low-frequency characteristics, the error is relatively large.
- the electromagnetic dual model is a model derived based on the principle of electromagnetic duality. Through the dual relationship between electric quantity and magnetic quantity, the magnetic circuit model of the device is converted into a circuit for representation, which has physical meaning.
- the electromagnetic dual model can be modeled with different fineness according to the applicable frequency range.
- the electromagnetic dual model requires a very complicated model topology in the simulation of high-frequency characteristics, and the requirements for the accuracy of the parameters are very high. It is difficult to obtain all Parameters, the detailed design parameters of the equipment are required.
- the electromagnetic dual model applied to low and medium frequencies has high accuracy.
- the inverse model is opposite to the positive model.
- the input of PT is the primary voltage
- the output is the secondary signal.
- the embodiment of the present application provides a PT primary voltage reconstruction method, device and equipment based on the inverse black box and inverse electromagnetic dual model, which is applied to the small current grounding system of the distribution network, and is used to solve the problem that the existing power system adopts
- the PT measures the voltage, and the PT is distorted during the measurement process, which leads to the technical problem of inaccurate measurement data.
- Fig. 1 is a flow chart of the steps of the PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model according to the embodiment of the present invention.
- the embodiment of the present invention provides a PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model, the method includes the following steps:
- the secondary voltage signal of the power system is collected through PT, and the secondary voltage signal is divided into low-frequency voltage component and high-frequency voltage component.
- step S1 the secondary voltage signal of the power system collected by the PT is mainly divided into low-frequency voltage components and high-frequency voltage components, which is convenient for subsequent steps to process the secondary voltage signal and convert it into a primary voltage.
- step S2 the high frequency voltage component of the primary voltage is mainly obtained through inverse black box model analysis and processing based on the high frequency voltage component obtained in step S1.
- the PT primary voltage reconstruction method based on the inverse black box and the inverse electromagnetic dual model realizes the reconstruction of the primary voltage signal based on the discrete secondary voltage signal data through the inverse black box model, which is convenient for obtaining the high frequency voltage component of the primary voltage, and the stability of the method good.
- step S3 the low-frequency voltage component of the primary voltage is mainly obtained through the analysis and processing of the inverse electromagnetic dual model based on the low-frequency voltage component obtained in step S1.
- the PT primary voltage reconstruction method based on the inverse black box and the inverse electromagnetic dual model realizes the primary voltage reconstruction based on the low-frequency component of the secondary voltage signal considering deep saturation through the inverse electromagnetic dual model, and the parameter acquisition method of the inverse electromagnetic dual model is mature , without a large amount of on-site measured data for training before modeling, and the calculation is simplified.
- the primary voltage of the power system is obtained mainly based on the addition and integration of the high-frequency voltage of the primary voltage in step S2 and the low-frequency voltage component of the primary voltage in step S3.
- the PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model processes the secondary voltage signal collected by the PT to obtain the primary voltage, which avoids the problem of inaccurate measurement data caused by distortion during the PT measurement of the power system.
- the PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model can reconstruct the high-frequency transient state of the PT primary side, and can also reconstruct the low-frequency transient overvoltage of the PT primary side.
- a PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model provided by the present invention the steps include: collecting the secondary voltage signal of the power system through the PT, and dividing the secondary voltage signal into low-frequency voltage components and high-frequency components high-frequency voltage component; for the high-frequency voltage component, the inverse black box model is used to reconstruct the primary voltage, and the high-frequency voltage component of the primary voltage is obtained; for the low-frequency voltage component, the inverse electromagnetic dual model is used to reconstruct the primary voltage, and the low-frequency voltage component of the primary voltage is obtained; The primary voltage of the power system is obtained by integrating the high-frequency voltage component of the primary voltage and the low-frequency voltage component of the primary voltage.
- the PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model uses the inverse black box model and the inverse electromagnetic dual model to process the high-frequency voltage component and low-frequency voltage component divided by the secondary voltage signal collected by the PT respectively, and obtains a primary
- the high-frequency voltage component of the voltage and the low-frequency voltage component of the primary voltage are added to obtain the primary voltage.
- the obtained primary voltage is not affected by the distortion in the PT acquisition process, and the data accuracy is high; it solves the problem of using PT to measure voltage in the existing power system. During the measurement process, PT is distorted, which leads to technical problems of inaccurate measurement data.
- Fig. 2 is a flow chart of the signal division steps of the PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model according to the embodiment of the present invention.
- dividing the secondary voltage signal into a low-frequency voltage component and a high-frequency voltage component includes:
- the secondary voltage signal is processed by Fourier transform to obtain the frequency domain form of the secondary voltage signal
- the low frequency domain of the secondary voltage signal and the high frequency domain of the secondary voltage signal are respectively inversely Fourier transformed to obtain corresponding low frequency voltage components and high frequency voltage components.
- the secondary voltage signal is mainly divided into low-frequency voltage components and high-frequency voltage components. Specifically: FFT converts the secondary voltage signal from the time domain signal to the frequency domain signal, and then uses the transition frequency f s to select, if the frequency is greater than the transition frequency f s , it is the high frequency frequency domain of the secondary voltage signal, and is less than or equal to the transition frequency f s is the low-frequency frequency domain quantity of the secondary voltage signal; the high-frequency voltage component in the time domain corresponding to the secondary voltage signal can be obtained by combining the components with a frequency greater than the transition frequency f s and performing inverse Fourier transform (iFFT).
- iFFT inverse Fourier transform
- the low-frequency voltage component in the time domain corresponding to the secondary voltage signal can be obtained by combining the components less than or equal to the transition frequency f s and performing iFFT.
- Low-frequency voltage components and high-frequency voltage components are distinguished by inversely calculating the transition frequency f s .
- the transition frequency f s depends on the measurement results of the scattering parameters of the voltage transfer characteristics of the PT. Generally, the transition frequency f s is much smaller than the first resonance point of the voltage transfer characteristics of the first PT changing with frequency, and generally needs to be less than 0.1 times the Frequency point frequency. Thus, the transition frequency f s can be limited according to requirements, and there is no limitation here.
- the steps of reconstructing the primary voltage by using the inverse black-box model for the high-frequency voltage component, and obtaining the high-frequency voltage component of the primary voltage include:
- the high-frequency voltage component is used as the input of the inverse black-box model, and the high-frequency voltage component is reconstructed and transformed through the transfer function of the inverse black-box model, and the inverse black-box model outputs the high-frequency voltage component of the primary voltage;
- reconstructing and transforming the high-frequency voltage component through the transfer function of the inverse black-box model includes:
- the discrete voltage reconstruction function is calculated in an iterative manner to obtain the reconstructed high-frequency voltage component of the primary voltage
- the discrete voltage reconstruction function is:
- x is the reference variable symbol
- k and k-1 are the time points of the kth and k-1th high-frequency voltage components respectively
- A is the N ⁇ N diagonal matrix of transfer function poles
- B is N ⁇ N 1 array
- ⁇ t is the time interval between the kth high-frequency voltage component and the k-1th high-frequency voltage component
- C is a 1 ⁇ N array of zero points of the transfer function
- D is a constant item.
- the inverse black-box model mainly reconstructs the high-frequency component of the primary voltage based on the high-frequency voltage component of the secondary signal.
- the voltage transfer characteristics of the PT primary voltage and secondary voltage signals can be obtained, that is, H m (s):
- v sh (s) is the secondary high-frequency high-voltage component
- v ph (s) is the high-frequency component of the primary voltage
- S 11 , S 12 , S 21 , and S 22 are matrix elements of the scattering matrix S.
- H i (s) C(sI-A) -1 B+D+Es, where I is N*N
- I is N*N
- D and E correspond to d and e respectively; in the scattering matrix, E is usually equal to 0.
- a new variable x can be defined to introduce the high-frequency component v ph of the primary voltage and the high-frequency voltage component v sh of the secondary signal.
- ⁇ , ⁇ , and ⁇ are all introduced variables, which are meaningless and easy to read.
- the simplified state variable x k is related to the input variable v sh(k) obtained at the same time point. Therefore, it is necessary to introduce a new state variable x k ' to avoid the contradiction of iterative calculation.
- the input variable of the inverse black box model is the high frequency and high voltage component of the secondary signal, and the output variable of the inverse black box model is reconstructed to obtain the primary voltage.
- the steps of reconstructing the primary voltage using the inverse electromagnetic dual model for the low-frequency voltage component, and obtaining the low-frequency voltage component of the primary voltage include:
- the low-frequency voltage component is used as the input of the inverse electromagnetic dual model, and the low-frequency voltage component is reconstructed through the flux linkage conservation of the inverse electromagnetic dual model and Kirchhoff's current-voltage law, and the inverse electromagnetic dual model outputs the primary voltage low-frequency voltage component;
- v pl nv m1 + R s1 i pl ;
- v m1 v Ls +v m2 ;
- v pl is the low-frequency voltage component of the primary voltage
- n is the turns ratio of the inverse electromagnetic dual model
- v m1 is the voltage of the first excitation branch in the inverse electromagnetic dual model
- v m2 is the second excitation in the inverse electromagnetic dual model
- the voltage of the branch v Ls is the voltage at both ends of the leakage inductance in the inverse electromagnetic dual model
- R s1 is the resistance of the primary winding in the inverse electromagnetic dual model
- i pl is the primary current of the inverse electromagnetic dual model
- i m1 is the inverse electromagnetic dual model
- i Ls is the current flowing through both ends of the leakage inductance in the inverse electromagnetic dual model.
- FIG. 3 is a schematic diagram of an inverse electromagnetic dual model of a PT primary voltage reconstruction method based on an inverse black box and an inverse electromagnetic dual model according to an embodiment of the present invention.
- the inverse electromagnetic dual model is mainly used to reconstruct the low-frequency voltage component of the primary voltage. It is derived from the forward electromagnetic dual model of PT, as shown in Figure 3, the PT low-frequency electromagnetic dual model, where R s1 and R s2 are the resistance of the primary winding of the reverse electromagnetic dual model and the resistance of the secondary winding of the reverse electromagnetic dual model resistance; L s is the leakage inductance of the inverse electromagnetic dual model. The leakage inductance and the resistance of the winding are constant, while the two magnetizing inductances are L m1 and L m2 in Figure 3 and are highly nonlinear. L m1 and L m2 are related to the magnetic permeability of different parts of the iron core.
- the shunt resistances R m1 and R m2 of the inverse electromagnetic dual model represent the core loss of the PT, which are much larger than the magnetization resistance.
- N 0 , N 1 and N 2 are the number of reference turns, the number of turns of the PT primary winding and the number of turns of the secondary winding, respectively.
- v pl , v sl and i pl are the measured terminal voltage and primary current at both ends of the two windings respectively;
- R L and i s are the load and load current respectively;
- i Ls is the current flowing through the leakage inductance;
- v m1 , v m2 , i m1 , i m2 are the voltage and current of excitation branch 1 and 2 respectively;
- i L1 , i R1 , i L2 , i R2 are the currents flowing through L m1 , R m1 , L m2 , R m2 respectively;
- i m1 and im2 are the currents flowing through magnetizing branches 1 and 2, respectively.
- the inverse electromagnetic dual model is derived from the relationship between voltage and current in the forward electromagnetic dual model.
- the input variable is the low-frequency voltage component of the secondary signal
- the output variable is the low-frequency voltage component of the primary voltage.
- the primary voltage The reconstruction of low-frequency voltage components is as follows:
- t 1 is the duration of integration
- ⁇ (0) is the initial value of ⁇
- the ⁇ -i curve of magnetizing inductance can be obtained through no-load test and saturation test. Then the current flowing through the magnetizing resistance is calculated by the formula, and then the current flowing through the magnetization branch 2 is calculated by the formula.
- i L1 , i R1 and i m1 can be calculated in the same way. in,
- the leakage inductance is constant.
- the current flowing through the leakage inductance is equal to i m2 . Therefore, the flux linkage and voltage ( ⁇ Ls and v Ls ) at both ends of the leakage inductance can be calculated by the following beam formula, respectively, and the formula is:
- ⁇ m1 and v m1 are then calculated with and , respectively.
- ⁇ m1 is the flux linkage of magnetization branch 1 in the inverse electromagnetic dual model
- ⁇ m2 is the flux linkage of magnetization branch 2 in the inverse electromagnetic dual model
- ⁇ Ls is the flux linkage of leakage inductance in the inverse electromagnetic dual model.
- the resistance, inductance and turns ratio of PT are measured by testing or provided by the equipment manufacturer.
- the voltage across the secondary winding is measured by a PT on site. Therefore, it can be directly used to reconstruct the low-frequency voltage component of the primary voltage of the PT. Converted to a sum by using trapezoidal integration and central difference equations for primary voltage low-frequency voltage component reconstruction based on low-frequency voltage components of discrete quadratic signals.
- ⁇ (k), V(k), V Ls (k) and I m2 (k) are the discrete forms of ⁇ (t), v(t), v Ls (t) and im2 (t), respectively.
- k 1, 2, 3, . . .
- Figure 4 is a comparison diagram of the PT primary voltage reconstruction method based on the inverse black box and the inverse electromagnetic dual model and the distorted signal according to the embodiment of the present invention
- Figure 5 is a comparison diagram based on the inverse black box and the The comparison diagram of the PT primary voltage reconstruction method and the distorted signal of the inverse electromagnetic dual model.
- the PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model is used for the secondary voltage signal
- Perform reconstruction processing specifically: in the low-frequency transient ferromagnetic resonance overvoltage condition,
- Figure 4 shows the comparison of the actual primary voltage, the secondary distortion signal, and the primary voltage after reconstruction, which proves that the The low-frequency accuracy of the primary voltage measured by the PT primary voltage reconstruction method of the box and the inverse electromagnetic dual model, and the measurement accuracy meets the site requirements. It can be seen from Figure 4 that under ferromagnetic resonance, PT is saturated, and the secondary side signal is significantly distorted.
- the primary side voltage can be reconstructed through the PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model, and The result almost coincides with the actual primary voltage.
- Fig. 5 shows the comparison of the actual primary voltage, the secondary distortion signal and the reconstructed primary voltage, which proves that the PT primary voltage reconstruction method measured by the inverse black box and inverse electromagnetic dual model is accurate
- the high-frequency accuracy of the primary voltage and the accurate measurement accuracy meet the requirements of the site; it can be seen from Figure 5 that under the lightning impact, the frequency dependence of the PT makes the secondary side signal significantly distorted.
- the PT primary voltage reconstruction method of the model can reconstruct the accurate primary lightning voltage, which almost coincides with the applied lightning impulse.
- Fig. 6 is a frame diagram of a PT primary voltage reconstruction device based on an inverse black box and an inverse electromagnetic dual model according to an embodiment of the present invention.
- the embodiment of the present invention also provides a PT primary voltage reconstruction device based on the inverse black box and inverse electromagnetic dual model, including: a frequency component extraction module 10, a high-frequency inverse calculation module 20, and a low-frequency inverse calculation module 30 and integration module 40;
- the frequency component extraction module 10 is used to collect the power system through the PT, and divide the secondary voltage signal into a low-frequency voltage component and a high-frequency voltage component;
- the high-frequency inverse calculation module 20 is used to reconstruct the primary voltage of the high-frequency voltage component using an inverse black-box model to obtain the high-frequency voltage component of the primary voltage;
- the low-frequency inverse calculation module 30 is used to reconstruct the primary voltage of the low-frequency voltage component using the inverse electromagnetic dual model to obtain the low-frequency voltage component of the primary voltage;
- the integration module 40 is used to integrate the high-frequency voltage component of the primary voltage and the low-frequency voltage component of the primary voltage to obtain the primary voltage of the power system.
- the high-frequency inverse calculation module 20 is also used to use the high-frequency voltage component as the input of the inverse black-box model, and reconstruct and transform the high-frequency voltage component through the transfer function of the inverse black-box model, and the inverse black-box
- the model outputs the primary voltage high-frequency voltage component
- v ph (s) H m -1 (s)v sh (s), where v sh (s) is the input variable of the inverse black box model, and v ph (s) is the output of the inverse black box model variable, H m -1 (s) is the transfer function of the inverse black-box model;
- the high-frequency inverse calculation module 20 includes a conversion sub-module and a calculation sub-module;
- the conversion sub-module is used to perform fitting conversion on the transfer function to obtain the state equation of the transfer function; and introduce the variable x and the central difference method to convert the state equation to obtain the discrete voltage reconstruction function;
- the calculation sub-module is used to calculate the discrete voltage reconstruction function in an iterative manner to obtain the reconstructed high-frequency voltage component of the primary voltage;
- the discrete voltage reconstruction function is:
- x is the reference variable symbol
- k and k-1 are the time points of the kth and k-1th high-frequency voltage components respectively
- A is the N ⁇ N diagonal matrix of transfer function poles
- B is N ⁇ N 1 array
- ⁇ t is the time interval between the kth high-frequency voltage component and the k-1th high-frequency voltage component
- C is a 1 ⁇ N array of zero points of the transfer function
- D is a constant term.
- the low-frequency inverse calculation module 30 is also used to use the low-frequency voltage component as the input of the inverse electromagnetic dual model, and the low-frequency voltage component is reconstructed through the flux linkage conservation of the inverse electromagnetic dual model and Kirchhoff's current-voltage law. Structural transformation, the inverse electromagnetic dual model outputs the low-frequency voltage component of the primary voltage;
- v pl nv m1 + R s1 i pl ;
- v m1 v Ls +v m2 ;
- v pl is the low-frequency voltage component of the primary voltage
- n is the turns ratio of the inverse electromagnetic dual model
- v m1 is the voltage of the first excitation branch in the inverse electromagnetic dual model
- v m2 is the second excitation in the inverse electromagnetic dual model
- the voltage of the branch v Ls is the voltage at both ends of the leakage inductance in the inverse electromagnetic dual model
- R s1 is the resistance of the primary winding in the inverse electromagnetic dual model
- i pl is the primary current of the inverse electromagnetic dual model
- i m1 is the inverse electromagnetic dual model
- i Ls is the current flowing through both ends of the leakage inductance in the inverse electromagnetic dual model.
- modules in the device in the second embodiment correspond to the steps in the method in the first embodiment, and the steps in the method in the first embodiment have been described in detail in the first embodiment, and the second embodiment will not refer to the steps in the device The contents of the modules are described in detail.
- An embodiment of the present invention provides a PT primary voltage reconstruction device based on an inverse black box and an inverse electromagnetic dual model, including a processor and a memory;
- a memory for storing program codes and transmitting the program codes to the processor
- the processor is configured to execute the above-mentioned PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model according to the instructions in the program code.
- the processor is configured to execute the steps in the embodiment of the above-mentioned PT primary voltage reconstruction method based on the inverse black box and inverse electromagnetic dual model according to the instructions in the program code.
- the processor executes the computer program, the functions of the modules/units in the above system/device embodiments are realized.
- a computer program can be divided into one or more modules/units, and one or more modules/units are stored in a memory and executed by a processor to complete the present application.
- One or more modules/units may be a series of computer program instruction segments capable of accomplishing specific functions, and the instruction segments are used to describe the execution process of the computer program in the terminal device.
- the terminal device may be a computing device such as a desktop computer, a notebook, a handheld computer, or a cloud server.
- a terminal device may include, but is not limited to, a processor and a memory. Those skilled in the art can understand that this does not constitute a limitation to the terminal device, and may include more or less components than those shown in the illustration, or combine certain components, or different components, for example, the terminal device may also include input and output devices, Network access devices, buses, etc.
- the so-called processor can be a central processing unit (Central Processing Unit, CPU), and can also be other general-purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), off-the-shelf Programmable gate array (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.
- a general-purpose processor may be a microprocessor, or the processor may be any conventional processor, or the like.
- the storage may be an internal storage unit of the terminal device, such as a hard disk or memory of the terminal device.
- the memory can also be an external storage device of the terminal device, such as a plug-in hard disk equipped on the terminal device, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash memory card (Flash Card), etc. .
- the memory may also include both an internal storage unit of the terminal device and an external storage device.
- the memory is used to store computer programs and other programs and data required by the terminal device.
- the memory can also be used to temporarily store data that has been output or will be output.
- the disclosed system, device and method can be implemented in other ways.
- the device embodiments described above are only illustrative.
- the division of the units is only a logical function division. In actual implementation, there may be other division methods.
- multiple units or components can be combined or May be integrated into another system, or some features may be ignored, or not implemented.
- the mutual coupling or direct coupling or communication connection shown or discussed may be through some interfaces, and the indirect coupling or communication connection of devices or units may be in electrical, mechanical or other forms.
- the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.
- each functional unit in each embodiment of the present invention may be integrated into one processing unit, each unit may exist separately physically, or two or more units may be integrated into one unit.
- the above-mentioned integrated units can be implemented in the form of hardware or in the form of software functional units.
- the integrated unit is realized in the form of a software function unit and sold or used as an independent product, it can be stored in a computer-readable storage medium.
- the computer software product is stored in a storage medium , including several instructions to make a computer device (which may be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the method described in each embodiment of the present invention.
- the aforementioned storage media include: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), magnetic disk or optical disc, etc., which can store program codes. .
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Abstract
一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法，包括通过PT采集电力系统的二次电压信号并将其分为低频电压分量和高频电压分量（S1）；对高频电压分量采用逆黑盒模型进行重构一次电压，得到一次电压高频电压分量（S2）；对低频电压分量采用逆电磁对偶模型进行重构一次电压，得到一次电压低频电压分量（S3）；将一次电压高频电压分量和一次电压低频电压分量整合，得到电力系统的一次电压（S4）。方法通过对PT采集二次电压信号划分的高频电压分量和低频电压分量分别采用逆黑盒模型和逆电磁对偶模型处理，得到一次电压高频电压分量和一次电压低频电压分量后将其相加得到一次电压，得到的一次电压不受PT采集过程中失真的影响，数据准确率高。
Description
本申请要求于2021年12月31日提交中国专利局、申请号为202111679244.3、发明名称为“基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
本发明涉及测量技术领域，尤其涉及一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法、装置及设备。
电压测量及其在线监测是电力系统中计量、故障诊断和故障保护可靠运行的关键。实测电压波形是电力系统中包含信息最多、最具说服力的波形之一。在35kV及以下的配网中，电压系统的电压往往通过电磁式电压互感器(Potential transformer，PT)进行测量。PT是一种仪用变压器，PT的一次侧绕组与电网直接相连，PT的二次侧绕组与计量仪表相连，PT的一次绕组与PT的二次绕组之间没有直接的电路连接而是通过磁场进行耦合测量。因此，PT能够通过磁耦合实现与一次电力系统的电磁隔离，并且成本较低、测量准确、安全可靠。在电力系统中，与电压相关的故障诊断和故障保护依赖于PT二次侧输出的准确的电压信号。
PT工作在其额定频率(50/60Hz)和额定电压范围内时，可以提供准确稳定的测量结果，其电压传递特性恒定，一次电压与二次电压之间几乎没有相位差，且幅值之比为匝数比。然而，当PT一次侧(一次绕组)被高频暂态电压或低频过电压激励时，PT的二次侧信号可能会失真，与原始一次侧电压呈现显著差异，这意味着PT在这些暂态电压激励下提供的暂态电压测量结果非常不准确。失真的PT二次信号对基于电压信号的故障诊断和保护等操作造成潜在隐患。同时，失真电压信号会严重误导事故后的分析及复盘。
发明内容
本发明实施例提供了一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法、装置及设备，用于解决现有电力系统采用PT测量电压，在测量过程中PT存在失真情况，导致测量数据不准确的技术问题。
为了实现上述目的，本发明实施例提供如下技术方案：
一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法，包括以下步骤：
通过PT采集电力系统的二次电压信号，并对所述二次电压信号分为低频电压分量和高频电压分量；
对所述高频电压分量采用逆黑盒模型进行重构一次电压，得到一次电压高频电压分量；
对所述低频电压分量采用逆电磁对偶模型进行重构一次电压，得到一次电压低频电压分量；
将所述一次电压高频电压分量和所述一次电压低频电压分量整合，得到电力系统的一次电压。
优选地，对所述二次电压信号分为低频电压分量和高频电压分量包括：
对所述二次电压信号采用傅里叶变换处理，得到二次电压信号频域形式；
对所述二次电压信号频域形式中的频率是否大于过渡频率划分为二次电压信号低频频域和二次电压信号高频频域；
分别对所述二次电压信号低频频域和所述二次电压信号高频频域采用傅里叶逆变换，得到对应的低频电压分量和高频电压分量。
优选地，对所述高频电压分量采用逆黑盒模型进行重构一次电压，得到一次电压高频电压分量的步骤包括：
将所述高频电压分量作为逆黑盒模型的输入，通过逆黑盒模型的传递函数对所述高频电压分量进行重构变换，逆黑盒模型输出一次电压高频电压分量；
其中，所述传递函数为v
ph(s)＝H
m
-1(s)v
sh(s)，式中，v
sh(s)为逆黑盒模型的输入变量，v
ph(s)为逆黑盒模型输出变量，H
m
-1(s)为逆黑盒模型的传递函 数。
优选地，通过逆黑盒模型的传递函数对所述高频电压分量进行重构变换包括：
对所述传递函数进行拟合转换，得到传递函数的状态方程；
引入变量x和中心差分法对所述状态方程进行转换，得到离散电压重构函数；
采用迭代方式对所述离散电压重构函数进行计算，得到重构的一次电压高频电压分量；
其中，所述离散电压重构函数为：
v
ph(k)＝Cx
k+Dv
sh(k)
式中，x为引用变量符号，k、k-1分别为高频电压分量中第k个、k-1个的时刻点，A为传递函数极点的N×N对角矩阵，B为N×1数组，Δt为第k个高频电压分量与第k-1个高频电压分量之间的时间间隔，C为传递函数零点的1×N的数组，D为常数项。
优选地，对所述低频电压分量采用逆电磁对偶模型进行重构一次电压，得到一次电压低频电压分量的步骤包括：
将所述低频电压分量作为逆电磁对偶模型的输入，通过逆电磁对偶模型的磁链守恒以及基尔霍夫电流电压定律对所述低频电压分量进行重构变换，逆电磁对偶模型输出一次电压低频电压分量；
其中，所述基尔霍夫电流电压定律为：
v
pl＝nv
m1+R
s1i
pl；
v
m1＝v
Ls+v
m2；
式中，v
pl为一次电压低频电压分量，n为逆电磁对偶模型的匝数比，v
m1为逆电磁对偶模型中第一励磁支路的电压，v
m2为逆电磁对偶模型中第二励磁支路的电压，v
Ls为逆电磁对偶模型中漏感两端的电压，R
s1为逆电磁 对偶模型中一次绕组的电阻，i
pl为逆电磁对偶模型的一次电流，i
m1为逆电磁对偶模型中流过第一励磁支路的电流，i
Ls为流过逆电磁对偶模型中漏感两端的电流。
优选地，该基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法包括：将所述一次电压高频电压分量与所述一次电压低频电压分量相加整合，得到电力系统的一次电压。
本发明还提供一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构装置，包括：频率分量提取模块、高频反算模块、低频反算模块和整合模块；
所述频率分量提取模块，用于通过PT采集电力系统的二次电压信号，并对所述二次电压信号分为低频电压分量和高频电压分量；
所述高频反算模块，用于对所述高频电压分量采用逆黑盒模型进行重构一次电压，得到一次电压高频电压分量；
所述低频反算模块，用于对所述低频电压分量采用逆电磁对偶模型进行重构一次电压，得到一次电压低频电压分量；
所述整合模块，用于将所述一次电压高频电压分量和所述一次电压低频电压分量整合，得到电力系统的一次电压。
优选地，所述高频反算模块还用于将所述高频电压分量作为逆黑盒模型的输入，通过逆黑盒模型的传递函数对所述高频电压分量进行重构变换，逆黑盒模型输出一次电压高频电压分量；
所述传递函数为v
ph(s)＝H
m
-1(s)v
sh(s)，式中，v
sh(s)为逆黑盒模型的输入变量，v
ph(s)为逆黑盒模型输出变量，H
m
-1(s)为逆黑盒模型的传递函数；
其中，所述高频反算模块包括转换子模块和计算子模块；
所述转换子模块，用于对所述传递函数进行拟合转换，得到传递函数的状态方程；并引入变量x和中心差分法对所述状态方程进行转换，得到离散电压重构函数；
所述计算子模块，用于采用迭代方式对所述离散电压重构函数进行计算，得到重构的一次电压高频电压分量；
其中，所述离散电压重构函数为：
v
ph(k)＝Cx
k+Dv
sh(k)
式中，x为引用变量符号，k、k-1分别为高频电压分量中第k个、k-1个的时刻点，A为传递函数极点的N×N对角矩阵，B为N×1数组，Δt为第k个高频电压分量与第k-1个高频电压分量之间的时间间隔，C为传递函数零点的1×N的数组，D为常数项。
优选地，所述低频反算模块还用于将所述低频电压分量作为逆电磁对偶模型的输入，通过逆电磁对偶模型的磁链守恒以及基尔霍夫电流电压定律对所述低频电压分量进行重构变换，逆电磁对偶模型输出一次电压低频电压分量：
其中，所述基尔霍夫电流电压定律为：
v
pl＝nv
m1+R
s1i
pl；
v
m1＝v
Ls+v
m2；
式中，v
pl为一次电压低频电压分量，n为逆电磁对偶模型的匝数比，v
m1为逆电磁对偶模型中第一励磁支路的电压，v
m2为逆电磁对偶模型中第二励磁支路的电压，v
Ls为逆电磁对偶模型中漏感两端的电压，R
s1为逆电磁对偶模型中一次绕组的电阻，i
pl为逆电磁对偶模型的一次电流，i
m1为逆电磁对偶模型中流过第一励磁支路的电流，i
Ls为流过逆电磁对偶模型中漏感两端的电流。
本发明还提供一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构设备，包括处理器以及存储器；
所述存储器，用于存储程序代码，并将所述程序代码传输给所述处理器；
所述处理器，用于根据所述程序代码中的指令执行上述所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法。
从以上技术方案可以看出，本发明实施例具有以下优点：该基于逆黑 盒及逆电磁对偶模型的PT一次电压重构方法、装置及设备，该方法步骤包括：通过PT采集电力系统的二次电压信号，并对二次电压信号分为低频电压分量和高频电压分量；对高频电压分量采用逆黑盒模型进行重构一次电压，得到一次电压高频电压分量；对低频电压分量采用逆电磁对偶模型进行重构一次电压，得到一次电压低频电压分量；将一次电压高频电压分量和一次电压低频电压分量整合，得到电力系统的一次电压。该基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法通过对PT采集二次电压信号划分的高频电压分量和低频电压分量分别采用逆黑盒模型和逆电磁对偶模型处理，得到一次电压高频电压分量和一次电压低频电压分量后将其相加得到一次电压，得到的一次电压不受PT采集过程中失真的影响，数据准确率高；解决了现有电力系统采用PT测量电压，在测量过程中PT存在失真情况，导致测量数据不准确的技术问题。
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动性的前提下，还可以根据这些附图获得其它的附图。
图1为本发明实施例所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法的步骤流程图；
图2为本发明实施例所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法信号划分的步骤流程图；
图3为本发明实施例所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法逆电磁对偶模型的示意图；
图4为本发明实施例所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法与失真信号的对比图；
图5为本发明另一实施例所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法与失真信号的对比图；
图6为本发明实施例所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构装置的框架图。
为使得本发明的发明目的、特征、优点能够更加的明显和易懂，下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，下面所描述的实施例仅仅是本发明一部分实施例，而非全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其它实施例，都属于本发明保护的范围。
本申请的术语解释如下：
电磁式电压互感器是通过变压器实现电磁隔离的电压测量装置，也是一种仪用变压器，基本原理与变压器完全相同。
在线监测指的是在被测设备处于运行的条件下，对设备的状况进行连续或定时的监测，通常是自动进行的。
PT一次侧指的是PT一次侧绕组(高压绕组)与电网直接相连。
PT一次电压指的是PT一次绕组两端电压。
PT二次侧指的是PT二次侧绕组(低压绕组)与计量装置等直接相连。
PT二次信号指的是PT二次绕组两端电压，也是被测量的信号。
黑盒模型指的是一种端口等效模型，不具备物理意义，仅能实现对端口特性与被建模设备一致。PT的黑盒模型在高频特性模拟方面具备显著的准确度，但是在低频特性上由于测量等因素，误差较大。
电磁对偶模型是基于电磁对偶原理推导而来的模型，通过电量及磁量的对偶关系，将设备的磁路模型转换成电路进行表征，具备物理意义。电磁对偶模型依据适用的频率范围可用不同精细度的模型，然而，该电磁对偶模型在高频特性模拟上需要非常复杂的模型拓扑，对参数的准确度的要求十分高，难以通过试验测量得到全部参数，需要设备的详细设计参数。应用于中低频的电磁对偶模型具备很高的精度。
逆模型是与正模型相对，以PT为例，PT的输入是一次电压，输出是 二次信号，基于一次电压得到二次信号的模型为正模型，而逆模型的输入是二次信号，输出是实际的一次电压，即基于二次信号输出一次电压的模型及为逆模型。
本申请实施例提供了一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法、装置及设备，应用于配电网的小电流接地系统上，用于解决了现有电力系统采用PT测量电压，在测量过程中PT存在失真情况，导致测量数据不准确的技术问题。
实施例一：
图1为本发明实施例所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法的步骤流程图。
如图1所示，本发明实施例提供了一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法，方法包括以下步骤：
S1.通过PT采集电力系统的二次电压信号，并对二次电压信号分为低频电压分量和高频电压分量。
需要说明的是，在步骤S1中主要是将PT采集电力系统的二次电压信号划分为低频电压分量和高频电压分量，便于后续步骤对二次电压信号处理转换为一次电压。
S2.对高频电压分量采用逆黑盒模型进行重构一次电压，得到一次电压高频电压分量。
需要说明的是，在步骤S2中主要是根据步骤S1获得的高频电压分量，再通过逆黑盒模型分析处理，得到一次电压高频电压分量。该基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法通过逆黑盒模型实现基于离散二次电压信号数据的一次电压信号的重建，便于得到一次电压高频电压分量，该方式稳定性好。
S3.对低频电压分量采用逆电磁对偶模型进行重构一次电压，得到一次电压低频电压分量。
需要说明的是，在步骤S3中主要是根据步骤S1获得的低频电压分量，再通过逆电磁对偶模型分析处理，得到一次电压低频电压分量。该基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法通过逆电磁对偶模型实现 考虑深度饱和的基于二次电压信号低频分量的一次电压重构，且该逆电磁对偶模型参数获取方法成熟，无需大量现场实测数据进行建模前的训练，计算简单化。
S4.将一次电压高频电压分量和一次电压低频电压分量整合，得到电力系统的一次电压。
需要说明的是，主要是根据步骤S2的一次电压高频电压和步骤S3的一次电压低频电压分量相加整合，得到电力系统的一次电压。该基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法对PT采集的二次电压信号进行处理，得到一次电压，避免了PT测量电力系统过程中失真导致测量数据不准确的问题，该基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法实现重构PT一次侧的高频暂态，也能重构PT一次侧的低频暂态过电压。
本发明提供的一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法，步骤包括：通过PT采集电力系统的二次电压信号，并对二次电压信号分为低频电压分量和高频电压分量；对高频电压分量采用逆黑盒模型进行重构一次电压，得到一次电压高频电压分量；对低频电压分量采用逆电磁对偶模型进行重构一次电压，得到一次电压低频电压分量；将一次电压高频电压分量和一次电压低频电压分量整合，得到电力系统的一次电压。该基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法通过对PT采集二次电压信号划分的高频电压分量和低频电压分量分别采用逆黑盒模型和逆电磁对偶模型处理，得到一次电压高频电压分量和一次电压低频电压分量后将其相加得到一次电压，得到的一次电压不受PT采集过程中失真的影响，数据准确率高；解决了现有电力系统采用PT测量电压，在测量过程中PT存在失真情况，导致测量数据不准确的技术问题。
图2为本发明实施例所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法信号划分的步骤流程图。
如图2所示，在本发明的一个实施例中，对二次电压信号分为低频电压分量和高频电压分量包括：
对二次电压信号采用傅里叶变换处理，得到二次电压信号频域形式；
对二次电压信号频域形式中的频率是否大于过渡频率划分为二次电压 信号低频频域和二次电压信号高频频域；
分别对二次电压信号低频频域和二次电压信号高频频域采用傅里叶逆变换，得到对应的低频电压分量和高频电压分量。
需要说明的是，主要是将二次电压信号分为低频电压分量及高频电压分量。具体为：FFT将二次电压信号从时域信号转换为频域信号，然后利用过渡频率f
s进行选择，若频率大于过渡频率f
s的为二次电压信号高频频域，小于等于过渡频率f
s的为二次电压信号低频频域量；将频率大于过渡频率f
s的分量集合起来再进行傅里叶逆变换(iFFT)即可得到与二次电压信号对应时域的高频电压分量。同理，将小于等于过渡频率f
s的分量集合起来进行iFFT即可得到与二次电压信号对应时域的低频电压分量。低频电压分量及高频电压分量采用反算过渡频率f
s进行区分。过渡频率f
s取决于PT的电压传递特性的散射参数测量结果，一般过渡频率f
s远小于第一个PT随频率变化的电压传递特性的第一个谐振点，且一般需要小于0.1倍的该频率点频率。由此，过渡频率f
s可以根据需求限定，此处不做限制。
在本发明的一个实施例中，对高频电压分量采用逆黑盒模型进行重构一次电压，得到一次电压高频电压分量的步骤包括：
将高频电压分量作为逆黑盒模型的输入，通过逆黑盒模型的传递函数对高频电压分量进行重构变换，逆黑盒模型输出一次电压高频电压分量；
其中，传递函数为v
ph(s)＝H
m
-1(s)v
sh(s)，式中，v
sh(s)为逆黑盒模型的输入变量，v
ph(s)为逆黑盒模型输出变量，H
m
-1(s)为逆黑盒模型的传递函数。
在本发明实施例中，通过逆黑盒模型的传递函数对高频电压分量进行重构变换包括：
对传递函数进行拟合转换，得到传递函数的状态方程；
引入变量x和中心差分法对状态方程进行转换，得到离散电压重构函数；
采用迭代方式对离散电压重构函数进行计算，得到重构的一次电压高频电压分量；
其中，离散电压重构函数为：
v
ph(k)＝Cx
k+Dv
sh(k)
式中，x为引用变量符号，k、k-1分别为高频电压分量中第k个、k-1个的时刻点，A为传递函数极点的N×N对角矩阵，B为N×1数组，Δt为第k个高频电压分量与第k-1个高频电压分量之间的时间间隔，C为传递函数零点的1×N的数组，D为常数项。
需要说明的是，逆黑盒模型主要是将基于二次信号的高频电压分量重构一次电压的高频分量，具体为：通过逆黑盒模型将高频电压分量中得到的数据采用散射矩阵进行化简，即可得到PT一次电压与二次电压信号的电压传递特性，即H
m(s)：
v
sh(s)为二次的高频高压分量，v
ph(s)为一次电压的高频分量，S
11、S
12、S
21、S
22均为散射矩阵S的矩阵元素。由此，可得到：v
sh(s)＝H
m(s)v
ph(s)，由于逆黑盒模型是通过二次电压信号重构一次电压的，因此，可改写为：v
ph(s)＝H
m
-1(s)v
sh(s)，由此可知，H
m
-1(s)就是逆黑盒模型的传递函数，通过矢量匹配法拟合H
m
-1(s)即可得到有理分式形式的H
i(s)：
式中，d为常数项，e为线性项系数，r
k和p
k为频域响应H
i(s)的零点和极点，N为拟合阶数。由有理分式形式的H
i(s)转化为传递函数的状态方程，即是：H
i(s)＝C(sI-A)
-1B+D+Es，式中，I为N*N的标准单位阵，对角元素全为1，其余为0；D和E分别对应于d和e；在散射矩阵中，E通常等于0。得到逆电压传递函数H
i(s)后，可定义一个新的变量x将一次电压的高频分量v
ph及二次信号的高频电压分量v
sh引入。x的定义为：x＝(sI-A)
-1Bv
sh，得到
v
ph＝Cx+Dv
sh。由于采集的二次电压信号是离散信号而非连续数据，而适用于连续数据，因此，采用中心差分法对状态方程进行转换，使其能够适用于离散数据得电压重构的离散电压重构函数，即是：
v
ph(k)＝Cx
k+Dv
sh(k)
对离散电压重构函数进行简化得到：x
k＝αx
k-1+λBv
sh(k)+μBv
sh(k-1)，v
ph(k)＝Cx
k+Dv
sh(k)；其中，
式中，λ、α、μ均为引入的变量，无意义，便于阅读。简化后的状态变量x
k与同一时间点得的输入变量v
sh(k)相关。因此，需要明引入了一个新的状态变量x
k'用以规避迭代计算得矛盾，状态变量x
k'为：x′
k＝x
k-λBv
sh(k)，对应的离散电压重构函数转换为离散状态空间方程(也称逆黑盒模型)，该离散状态空间方程为：
v
ph(k)＝Cx′
k+Gv
sh(k)，
G＝D+CλB，式中的G、
均为引入的变量，无意义，便于阅读；v
ph(k)为重构后输出的一次电压高频电压分量。逆黑盒模型的输入变量为二次信号的高频高压分量，逆黑盒模型的输出变量重构得到得一次电压。
在本发明的一个实施例中，对低频电压分量采用逆电磁对偶模型进行重构一次电压，得到一次电压低频电压分量的步骤包括：
将低频电压分量作为逆电磁对偶模型的输入，通过逆电磁对偶模型的磁链守恒以及基尔霍夫电流电压定律对低频电压分量进行重构变换，逆电磁对偶模型输出一次电压低频电压分量；
其中，基尔霍夫电流电压定律为：
v
pl＝nv
m1+R
s1i
pl；
v
m1＝v
Ls+v
m2；
式中，v
pl为一次电压低频电压分量，n为逆电磁对偶模型的匝数比，v
m1为逆电磁对偶模型中第一励磁支路的电压，v
m2为逆电磁对偶模型中第二励磁支路的电压，v
Ls为逆电磁对偶模型中漏感两端的电压，R
s1为逆电磁 对偶模型中一次绕组的电阻，i
pl为逆电磁对偶模型的一次电流，i
m1为逆电磁对偶模型中流过第一励磁支路的电流，i
Ls为流过逆电磁对偶模型中漏感两端的电流。
图3为本发明实施例所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法逆电磁对偶模型的示意图。
需要说明的是，逆电磁对偶模型主要是用于重构一次电压低频电压分量。其由PT的正向电磁对偶模型推导得到，如图3所示的PT低频电磁对偶模型，其中，R
s1和R
s2分别为逆电磁对偶模型一次绕组的电阻和逆电磁对偶模型二次绕组的电阻；L
s为逆电磁对偶模型的漏感。漏感和绕组的电阻是恒定的，而两个磁化电感分别为图3中的L
m1和L
m2且是高度非线性的。L
m1和L
m2与铁芯不同部位的磁导有关。逆电磁对偶模型的分流电阻R
m1和R
m2代表PT的磁芯损耗，它们远大于磁化阻抗。N
0、N
1和N
2分别为参考匝数、PT一次绕组匝数和二次绕组匝数。v
pl、v
sl和i
pl分别为测量的两个绕组两端的端电压和一次电流；R
L和i
s分别为负载和负载电流；i
Ls为流经漏感上电流；v
m1、v
m2、i
m1、i
m2分别为励磁支路1、2的电压和电流；i
L1、i
R1、i
L2、i
R2分别为流经L
m1、R
m1、L
m2、R
m2的电流；i
m1和i
m2分别是流经磁化支路1和2的电流。其中，假设N
0＝N
2，匝数比n＝N
1/N
2。
如图3所示，逆电磁对偶模型通过正向电磁对偶模型中电压电流的关系推导而来，其输入变量为二次信号的低频电压分量，而输出变量为一次电压低频电压分量，其一次电压低频电压分量重构具体为：
负载电流i
L是通过仪器测量，也可以通过负载阻抗和负载两端电压计算得到。因此，磁化支路2两端的电压的计算公式为：v
m2＝v
sl+i
sR
s2，磁链通过对电压积分获得。因此，磁化支路2上的磁链(λ
m2)计算公式为：
式中，t
1为积分的持续时间，λ(0)是λ的初始值，磁化电感的λ-i曲线可以通过空载测试和饱和测试获得。那么流过磁化电阻的电流用式计算，然后流过磁化支路2的电流用式计算。同样，i
L1、i
R1和i
m1可以采用相同的方式计算得到。其中，
在逆电磁对偶模型中，漏感是常数。流过漏感的电流等于i
m2。因此，漏感两端的磁链和电压(λ
Ls和v
Ls)可以分别通过如下梁式计算，公式为：
i
m2＝i
L2+i
R2，i
Ls＝i
m2+i
s，λ
Ls＝i
LsL
s；
然后分别用和计算λ
m1和v
m1。采用逆对偶导出模型中的磁链守恒定律为：λ
m1＝λ
Ls+λ
m2；v
m1＝v
Ls+v
m2，那么流经一次绕组的电流由i
pl＝(i
m1+i
Ls)/n获得，然后采用v
pl＝nv
m1+R
s1i
pl计算一次电压。式中，λ
m1为逆电磁对偶模型中磁化支路1的磁链，λ
m2为逆电磁对偶模型中磁化支路2的磁链，λ
Ls为逆电磁对偶模型中漏感的磁链。PT的电阻、电感、匝数比通过测试测量或由设备出厂商提供。二次绕组两端的电压由现场的PT测量。因此，可以直接用于重构PT的一次电压低频电压分量。通过使用梯形积分和中心差分方程来转换为和，用于基于离散二次信号的低频电压分量的一次电压低频电压分量重构。
其中Λ(k)、V(k)、V
Ls(k)和I
m2(k)分别是λ(t)、v(t)、v
Ls(t)和i
m2(t)的离散形式。k＝1，2，3，……。
图4为本发明实施例所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法与失真信号的对比图，图5为本发明另一实施例所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法与失真信号的对比图。
在本发明实施例中，该基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法对低频暂态铁磁谐振过电压工况和雷电冲击工况这两种失真信号的二次电压信号进行重构处理，具体如：在低频暂态铁磁谐振过电压工况中，图4给出了实际一次电压，二次失真信号及重构后一次电压的对比，证明了通过该基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法测量 的一次电压的低频精度，测量精度满足现场要求。由图4可知，在铁磁谐振下，PT饱和，二次侧信号显著失真，然而，通过该基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法能够重构得到一次侧电压，且结果几乎和实际一次侧电压重合。在雷电冲击工况中，图5给出了实际一次电压，二次失真信号及重构后一次电压的对比，证明了该于逆黑盒及逆电磁对偶模型的PT一次电压重构方法测量的一次电压的高频准确性，准确测量精度满足现场要求；由图5可知，在雷电冲击下，PT的频率依赖性使其二次侧信号发生显著失真，通过该基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法能够重构得到准确的一次侧雷电电压，与施加的雷电冲击几乎重合。
实施例二：
图6为本发明实施例所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构装置的框架图。
如图6所示，本发明实施例还提供一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构装置，包括：频率分量提取模块10、高频反算模块20、低频反算模块30和整合模块40；
频率分量提取模块10，用于通过PT采集电力系统的，并对二次电压信号分为低频电压分量和高频电压分量；
高频反算模块20，用于对高频电压分量采用逆黑盒模型进行重构一次电压，得到一次电压高频电压分量；
低频反算模块30，用于对低频电压分量采用逆电磁对偶模型进行重构一次电压，得到一次电压低频电压分量；
整合模块40，用于将一次电压高频电压分量和一次电压低频电压分量整合，得到电力系统的一次电压。
在本发明实施例中，高频反算模块20还用于将高频电压分量作为逆黑盒模型的输入，通过逆黑盒模型的传递函数对高频电压分量进行重构变换，逆黑盒模型输出一次电压高频电压分量；
传递函数为v
ph(s)＝H
m
-1(s)v
sh(s)，式中，v
sh(s)为逆黑盒模型的输入变量，v
ph(s)为逆黑盒模型输出变量，H
m
-1(s)为逆黑盒模型的传递函数；
其中，高频反算模块20包括转换子模块和计算子模块；
转换子模块，用于对传递函数进行拟合转换，得到传递函数的状态方程；并引入变量x和中心差分法对状态方程进行转换，得到离散电压重构函数；
计算子模块，用于采用迭代方式对离散电压重构函数进行计算，得到重构的一次电压高频电压分量；
其中，离散电压重构函数为：
v
ph(k)＝Cx
k+Dv
sh(k)
式中，x为引用变量符号，k、k-1分别为高频电压分量中第k个、k-1个的时刻点，A为传递函数极点的N×N对角矩阵，B为N×1数组，Δt为第k个高频电压分量与第k-1个高频电压分量之间的时间间隔，C为传递函数零点的1×N的数组，D为常数项。
在本发明实施例中，低频反算模块30还用于将低频电压分量作为逆电磁对偶模型的输入，通过逆电磁对偶模型的磁链守恒以及基尔霍夫电流电压定律对低频电压分量进行重构变换，逆电磁对偶模型输出一次电压低频电压分量；
其中，磁链守恒以及基尔霍夫电流电压定律为：
v
pl＝nv
m1+R
s1i
pl；
v
m1＝v
Ls+v
m2；
式中，v
pl为一次电压低频电压分量，n为逆电磁对偶模型的匝数比，v
m1为逆电磁对偶模型中第一励磁支路的电压，v
m2为逆电磁对偶模型中第二励磁支路的电压，v
Ls为逆电磁对偶模型中漏感两端的电压，R
s1为逆电磁对偶模型中一次绕组的电阻，i
pl为逆电磁对偶模型的一次电流，i
m1为逆电磁对偶模型中流过第一励磁支路的电流，i
Ls为流过逆电磁对偶模型中漏感两端的电流。
需要说明的是，实施例二装置中的模块对应于实施例一方法中的步骤，实施例一方法中的步骤已在实施例一中详细阐述了，在此实施例二中不再对装置中的模块内容进行详细阐述。
实施例三：
本发明实施例提供了一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构设备，包括处理器以及存储器；
存储器，用于存储程序代码，并将程序代码传输给处理器；
处理器，用于根据程序代码中的指令执行上述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法。
需要说明的是，处理器用于根据所程序代码中的指令执行上述的一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法实施例中的步骤。或者，处理器执行计算机程序时实现上述各系统/装置实施例中各模块/单元的功能。
示例性的，计算机程序可以被分割成一个或多个模块/单元，一个或者多个模块/单元被存储在存储器中，并由处理器执行，以完成本申请。一个或多个模块/单元可以是能够完成特定功能的一系列计算机程序指令段，该指令段用于描述计算机程序在终端设备中的执行过程。
终端设备可以是桌上型计算机、笔记本、掌上电脑及云端服务器等计算设备。终端设备可包括，但不仅限于，处理器、存储器。本领域技术人员可以理解，并不构成对终端设备的限定，可以包括比图示更多或更少的部件，或者组合某些部件，或者不同的部件，例如终端设备还可以包括输入输出设备、网络接入设备、总线等。
所称处理器可以是中央处理单元(Central Processing Unit，CPU)，还可以是其他通用处理器、数字信号处理器(Digital Signal Processor，DSP)、专用集成电路(Application Specific Integrated Circuit，ASIC)、现成可编程门阵列(Field-Programmable Gate Array，FPGA)或者其他可编程逻辑器件、分立门或者晶体管逻辑器件、分立硬件组件等。通用处理器可以是微处理器或者该处理器也可以是任何常规的处理器等。
存储器可以是终端设备的内部存储单元，例如终端设备的硬盘或内存。 存储器也可以是终端设备的外部存储设备，例如终端设备上配备的插接式硬盘，智能存储卡(Smart Media Card，SMC)，安全数字(Secure Digital，SD)卡，闪存卡(Flash Card)等。进一步地，存储器还可以既包括终端设备的内部存储单元也包括外部存储设备。存储器用于存储计算机程序以及终端设备所需的其他程序和数据。存储器还可以用于暂时地存储已经输出或者将要输出的数据。
所属领域的技术人员可以清楚地了解到，为描述的方便和简洁，上述描述的系统，装置和单元的具体工作过程，可以参考前述方法实施例中的对应过程，在此不再赘述。
在本申请所提供的几个实施例中，应该理解到，所揭露的系统，装置和方法，可以通过其它的方式实现。例如，以上所描述的装置实施例仅仅是示意性的，例如，所述单元的划分，仅仅为一种逻辑功能划分，实际实现时可以有另外的划分方式，例如多个单元或组件可以结合或者可以集成到另一个系统，或一些特征可以忽略，或不执行。另一点，所显示或讨论的相互之间的耦合或直接耦合或通信连接可以是通过一些接口，装置或单元的间接耦合或通信连接，可以是电性，机械或其它的形式。
所述作为分离部件说明的单元可以是或者也可以不是物理上分开的，作为单元显示的部件可以是或者也可以不是物理单元，即可以位于一个地方，或者也可以分布到多个网络单元上。可以根据实际的需要选择其中的部分或者全部单元来实现本实施例方案的目的。
另外，在本发明各个实施例中的各功能单元可以集成在一个处理单元中，也可以是各个单元单独物理存在，也可以两个或两个以上单元集成在一个单元中。上述集成的单元既可以采用硬件的形式实现，也可以采用软件功能单元的形式实现。
所述集成的单元如果以软件功能单元的形式实现并作为独立的产品销售或使用时，可以存储在一个计算机可读取存储介质中。基于这样的理解，本发明的技术方案本质上或者说对现有技术做出贡献的部分或者该技术方案的全部或部分可以以软件产品的形式体现出来，该计算机软件产品存储在一个存储介质中，包括若干指令用以使得一台计算机设备(可以是个人 计算机，服务器，或者网络设备等)执行本发明各个实施例所述方法的全部或部分步骤。而前述的存储介质包括：U盘、移动硬盘、只读存储器(ROM，Read-Only Memory)、随机存取存储器(RAM，Random Access Memory)、磁碟或者光盘等各种可以存储程序代码的介质。
以上所述，以上实施例仅用以说明本发明的技术方案，而非对其限制；尽管参照前述实施例对本发明进行了详细的说明，本领域的普通技术人员应当理解：其依然可以对前述各实施例所记载的技术方案进行修改，或者对其中部分技术特征进行等同替换；而这些修改或者替换，并不使相应技术方案的本质脱离本发明各实施例技术方案的精神和范围。
Claims (10)
- 一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法，其特征在于，包括以下步骤：通过PT采集电力系统的二次电压信号，并对所述二次电压信号分为低频电压分量和高频电压分量；对所述高频电压分量采用逆黑盒模型进行重构一次电压，得到一次电压高频电压分量；对所述低频电压分量采用逆电磁对偶模型进行重构一次电压，得到一次电压低频电压分量；将所述一次电压高频电压分量和所述一次电压低频电压分量整合，得到电力系统的一次电压。
- 根据权利要求1所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法，其特征在于，对所述二次电压信号分为低频电压分量和高频电压分量包括：对所述二次电压信号采用傅里叶变换处理，得到二次电压信号频域形式；对所述二次电压信号频域形式中的频率是否大于过渡频率划分为二次电压信号低频频域和二次电压信号高频频域；分别对所述二次电压信号低频频域和所述二次电压信号高频频域采用傅里叶逆变换，得到对应的低频电压分量和高频电压分量。
- 根据权利要求1所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法，其特征在于，对所述高频电压分量采用逆黑盒模型进行重构一次电压，得到一次电压高频电压分量的步骤包括：将所述高频电压分量作为逆黑盒模型的输入，通过逆黑盒模型的传递函数对所述高频电压分量进行重构变换，逆黑盒模型输出一次电压高频电压分量；其中，所述传递函数为v ph(s)＝H m -1(s)v sh(s)，式中，v sh(s)为逆黑盒模型的输入变量，v ph(s)为逆黑盒模型输出变量，H m -1(s)为逆黑盒模型的传递函数。
- 根据权利要求3所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法，其特征在于，通过逆黑盒模型的传递函数对所述高频电压分量进行重构变换包括：对所述传递函数进行拟合转换，得到传递函数的状态方程；引入变量x和中心差分法对所述状态方程进行转换，得到离散电压重构函数；采用迭代方式对所述离散电压重构函数进行计算，得到重构的一次电压高频电压分量；其中，所述离散电压重构函数为：
v ph(k)＝Cx k+Dv sh(k)式中，x为引用变量符号，k、k-1分别为高频电压分量中第k个、k-1个的时刻点，A为传递函数极点的N×N对角矩阵，B为N×1数组，Δt为第k个高频电压分量与第k-1个高频电压分量之间的时间间隔，C为传递函数零点的1×N的数组，D为常数项。 - 根据权利要求1所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法，其特征在于，对所述低频电压分量采用逆电磁对偶模型进行重构一次电压，得到一次电压低频电压分量的步骤包括：将所述低频电压分量作为逆电磁对偶模型的输入，通过逆电磁对偶模型的磁链守恒以及基尔霍夫电流电压定律对所述低频电压分量进行重构变换，逆电磁对偶模型输出一次电压低频电压分量；其中，所述基尔霍夫电流电压定律为：v pl＝nv m1+R s1i pl；v m1＝v Ls+v m2；
式中，v pl为一次电压低频电压分量，n为逆电磁对偶模型的匝数比，v m1为逆电磁对偶模型中第一励磁支路的电压，v m2为逆电磁对偶模型中第 二励磁支路的电压，v Ls为逆电磁对偶模型中漏感两端的电压，R s1为逆电磁对偶模型中一次绕组的电阻，i pl为逆电磁对偶模型的一次电流，i m1为逆电磁对偶模型中流过第一励磁支路的电流，i Ls为流过逆电磁对偶模型中漏感两端的电流。 - 根据权利要求1所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法，其特征在于，将所述一次电压高频电压分量和所述一次电压低频电压分量整合，得到电力系统的一次电压，包括：将所述一次电压高频电压分量与所述一次电压低频电压分量相加整合，得到电力系统的一次电压。
- 一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构装置，其特征在于，包括：频率分量提取模块、高频反算模块、低频反算模块和整合模块；所述频率分量提取模块，用于通过PT采集电力系统的二次电压信号，并对所述二次电压信号分为低频电压分量和高频电压分量；所述高频反算模块，用于对所述高频电压分量采用逆黑盒模型进行重构一次电压，得到一次电压高频电压分量；所述低频反算模块，用于对所述低频电压分量采用逆电磁对偶模型进行重构一次电压，得到一次电压低频电压分量；所述整合模块，用于将所述一次电压高频电压分量和所述一次电压低频电压分量整合，得到电力系统的一次电压。
- 根据权利要求7所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构装置，其特征在于，所述高频反算模块还用于将所述高频电压分量作为逆黑盒模型的输入，通过逆黑盒模型的传递函数对所述高频电压分量进行重构变换，逆黑盒模型输出一次电压高频电压分量；所述传递函数为v ph(s)＝H m -1(s)v sh(s)，式中，v sh(s)为逆黑盒模型的输入变量，v ph(s)为逆黑盒模型输出变量，H m -1(s)为逆黑盒模型的传递函数；其中，所述高频反算模块包括转换子模块和计算子模块；所述转换子模块，用于对所述传递函数进行拟合转换，得到传递函数的状态方程；并引入变量x和中心差分法对所述状态方程进行转换，得到 离散电压重构函数；所述计算子模块，用于采用迭代方式对所述离散电压重构函数进行计算，得到重构的一次电压高频电压分量；其中，所述离散电压重构函数为：
v ph(k)＝Cx k+Dv sh(k)式中，x为引用变量符号，k、k-1分别为高频电压分量中第k个、k-1个的时刻点，A为传递函数极点的N×N对角矩阵，B为N×1数组，Δt为第k个高频电压分量与第k-1个高频电压分量之间的时间间隔，C为传递函数零点的1×N的数组，D为常数项。 - 根据权利要求7所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构装置，其特征在于，所述低频反算模块还用于将所述低频电压分量作为逆电磁对偶模型的输入，通过逆电磁对偶模型的磁链守恒以及基尔霍夫电流电压定律对所述低频电压分量进行重构变换，逆电磁对偶模型输出一次电压低频电压分量；其中，所述基尔霍夫电流电压定律为：v pl＝nv m1+R s1i pl；v m1＝v Ls+v m2；
式中，v pl为一次电压低频电压分量，n为逆电磁对偶模型的匝数比，v m1为逆电磁对偶模型中第一励磁支路的电压，v m2为逆电磁对偶模型中第二励磁支路的电压，v Ls为逆电磁对偶模型中漏感两端的电压，R s1为逆电磁对偶模型中一次绕组的电阻，i pl为逆电磁对偶模型的一次电流，i m1为逆电磁对偶模型中流过第一励磁支路的电流，i Ls为流过逆电磁对偶模型中漏感两端的电流。 - 一种基于逆黑盒及逆电磁对偶模型的PT一次电压重构设备，其特征在于，包括处理器以及存储器；所述存储器，用于存储程序代码，并将所述程序代码传输给所述处理器；所述处理器，用于根据所述程序代码中的指令执行如权利要求1-6任意一项所述的基于逆黑盒及逆电磁对偶模型的PT一次电压重构方法。
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