Method for solving equivalent impedance and impedance frequency-dependent characteristic curve of equipment

Abstract

The invention discloses an equipment equivalent impedance and impedance frequency-dependent characteristic curve solving method, and belongs to the technical field of power generation. The problem that the equivalent impedance and the impedance frequency-dependent curve of existing equipment are difficult to model is solved. The method comprises the following steps: establishing a target equipment impedance network model, and simplifying the impedance network model by utilizing a circuit principle and Laplace transformation to obtain equivalent impedance; drawing a Bode diagram of the equivalent impedance by using software MATLAB; the coordinates of the Bode diagram are modified into linear coordinates, and the equivalent resistance, the equivalent reactance and the impedance frequency-dependent curve of the target equipment are solved through the Bode diagram in a linear coordinate system. The method is suitable for solving the equivalent impedance and the impedance frequency-dependent characteristic curve of the equipment.

Description

Technical Field

[0001] The invention belongs to the technical field of power generation. Background Art

[0002] Equivalent impedance plays an important role in power system analysis. It can be used to analyze the stability of the system, verify the heating principle, system subsynchronous oscillation, etc. When studying the problem of system subsynchronous oscillation, the impedance analysis method reduces the amount of calculation of the "curse of dimensionality" compared to the eigenvalue method. Compared with the complex torque method, its physical meaning is clear, that is, equivalent resistance and equivalent reactance, which are the inherent properties of the equipment itself and can comprehensively reflect the stability of the equipment.

[0003] Solving the equivalent impedance is the primary task of establishing an impedance model. Currently, the impedance modeling methods that have been demonstrated include the dq impedance model obtained by the dq axis linearization method and the sequence domain impedance model obtained by the harmonic linearization method. Both methods have their own advantages and disadvantages.

[0004] The dq impedance modeling method converts sinusoidal quantities into DC quantities and establishes an impedance state space. The dq axes are coupled to each other into four groups of channels, and the stability is judged by the Nyquist stability criterion. The advantages are clear principles and easy operation. The disadvantages are that it cannot handle unbalanced or distorted sources and loads. In the dq coordinate system, it is difficult to interpret and measure the impedance response. Only the four groups of channels can be independent, and it is mostly used in simple systems.

[0005] The sequence domain impedance modeling method is to add a small-amplitude harmonic disturbance voltage to the power frequency input voltage of the equipment port, derive its corresponding current response, and then obtain the harmonic equivalent impedance. The advantage is that it is not restricted by dq coordinate transformation, has low requirements on the system, and is suitable for "black-gray box" systems. The disadvantage is that the expression contains disturbance quantities, which is not easy to analyze as a whole, and is mostly applicable to three-phase stationary coordinate systems. Summary of the invention

[0006] The present invention aims to solve the problem that the equivalent impedance and the impedance-frequency curve of the existing equipment are difficult to model, and now provides a method for obtaining the equivalent impedance and the impedance-frequency curve of the equipment.

[0007] The present invention provides a method for obtaining an equivalent impedance of a device and an impedance frequency-dependent curve, the method comprising:

[0008] Step 1: Establish an impedance network model of the target device, simplify the impedance network model using circuit principles and Laplace transform to obtain equivalent impedance;

[0009] Step 2: Use MATLAB software to draw the Bode diagram of equivalent impedance;

[0010] Step 3: Change the coordinates of the Bode diagram to linear coordinates, and use the Bode diagram in the linear coordinate system to find the equivalent resistance, equivalent reactance and impedance frequency curve of the target device.

[0011] Furthermore, in the present invention, in step 1, the method for establishing the target device impedance network model is:

[0012] The impedance network models of different devices of the target device are established, and the impedance network models of different devices are connected according to the topological structure relationship of the target device system to obtain the impedance network model of the target device.

[0013] Furthermore, in the present invention, in step 1, the impedance network model is simplified by using circuit principles and Laplace transform to obtain an equivalent impedance:

[0014] The impedance network model is transformed into an incremental equation. In the incremental equation, the differential term is directly Laplace transformed:

[0015]

[0016] In the formula, A is the differential coefficient, B is the change, t is time, and s is the Laplace operator. The inductance and capacitance are Laplace transformed:

[0017]

[0018] Where L represents inductance and C represents capacitance. The original circuit is simplified to a simple RLC second-order circuit. The equivalent impedance is the ratio of the output voltage to the output current.

[0019] Calculate the equivalent impedance of the device:

[0020]

[0021] △u is the micro increment of the device output voltage, △i is the micro increment of the device output current, and z represents the equivalent impedance of the device.

[0022] Further, in the present invention, in step 2, the Bode diagram expression of the equivalent impedance is:

[0023]

[0024] In the formula, R is the equivalent resistance, X is the equivalent reactance, and Z is the equivalent impedance. For phase.

[0025]

[0026] Furthermore, in the present invention, in step 3, the method for modifying the coordinates of the Bode diagram into linear coordinates is:

[0027] The frequency logarithm of the abscissa of the amplitude-frequency characteristic curve and the phase-frequency characteristic curve in the Bode diagram is changed to a linear coordinate, and the unit is changed from rad / s to Hz; the ordinate of the amplitude-frequency characteristic curve is changed from dB to abs.

[0028] Further, in the present invention, in step 3, the equivalent resistance and equivalent reactance of the target device are:

[0029]

[0030] Where ψ is the phase of the impedance in the actual circuit.

[0031] The impedance modeling method described in the present invention has fewer constraints and restrictions. It converts the system mathematical model into an incremental equation form and only observes the apparent impedance, that is, the ratio of the output voltage to the current. It is not restricted by the coordinate system and only considers the output voltage and the output current. It is suitable for equations containing differential terms. When used in combination with the Laplace transform, the s-domain transfer function of the impedance can be directly established. After obtaining the impedance transfer function, the subsequent analysis can be carried out using the corresponding stability criterion. The impedance method is widely used in many fields. The proposal of this method can reduce the difficulty of establishing the impedance model and is of great significance to many fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flow chart of the method of the present invention;

[0033] Figure 2 This is the simplified equivalent circuit of the target device. DETAILED DESCRIPTION

[0034] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0035] Specific implementation method 1: refer to Figure 1 Specifically describe this embodiment, a method for obtaining a device equivalent impedance and an impedance-frequency characteristic curve described in this embodiment, a method for obtaining a device equivalent impedance and an impedance-frequency characteristic curve, the method comprising:

[0036] Step 1: Establish an impedance network model of the target device, simplify the impedance network model using circuit principles and Laplace transform to obtain equivalent impedance;

[0037] Step 2: Use MATLAB software to draw the Bode diagram of equivalent impedance;

[0038] Step 3: Change the coordinates of the Bode diagram to linear coordinates, and use the Bode diagram in the linear coordinate system to find the equivalent resistance, equivalent reactance and impedance frequency curve of the target device.

[0039] Furthermore, in the present invention, in step 1, the method for establishing the target device impedance network model is:

[0040] The impedance network models of different devices of the target device are established, and the impedance network models of different devices are connected according to the topological structure relationship of the target device system to obtain the impedance network model of the target device.

[0041] Furthermore, in the present invention, in step 1, the impedance network model is simplified by using circuit principles and Laplace transform to obtain an equivalent impedance:

[0042] The impedance network model is transformed into an incremental equation. In the incremental equation, the differential term is directly Laplace transformed:

[0043]

[0044] In the formula, A is the differential coefficient, B is the change, t is time, and s is the Laplace operator. The inductance and capacitance are Laplace transformed:

[0045]

[0046] Where L represents inductance and C represents capacitance. The original circuit is simplified to a simple RLC second-order circuit. The equivalent impedance is the ratio of the output voltage to the output current.

[0047] Calculate the equivalent impedance of the device:

[0048]

[0049] △u is the micro increment of the device output voltage, △i is the micro increment of the device output current, and z represents the equivalent impedance of the device.

[0050] Further, in the present invention, in step 2, the Bode diagram expression of the equivalent impedance is:

[0051]

[0052] In the formula, R is the equivalent resistance, X is the equivalent reactance, and Z is the equivalent impedance. For phase.

[0053]

[0054] Furthermore, in the present invention, in step 3, the method for modifying the coordinates of the Bode diagram into linear coordinates is:

[0055] The frequency logarithm of the abscissa of the amplitude-frequency characteristic curve and the phase-frequency characteristic curve in the Bode diagram is changed to a linear coordinate, and the unit is changed from rad / s to Hz; the ordinate of the amplitude-frequency characteristic curve is changed from dB to abs.

[0056] Further, in the present invention, in step 3, the equivalent resistance and equivalent reactance of the target device are:

[0057]

[0058] Where ψ is the phase of the impedance in the actual circuit.

[0059] Specifically, a method for obtaining an equivalent impedance curve of a device is provided. The method is to quantify the mathematical and physical equations of the device to be studied into an incremental equation form according to the change, assuming that the mathematical and physical equations of the device to be studied are linear in a small range, so as to obtain the incremental equation of the device to be studied.

[0060] In the incremental equation, the differential term is directly Laplace transformed as shown below:

[0061]

[0062] In the formula, A is the differential term coefficient, B is the change, t is time, and s is the Laplace operator. In the process of establishing the incremental equation, the differential component in the original equation should be directly converted into this form to facilitate subsequent analysis.

[0063] After that, the inductance and capacitance in the formula are transformed into complex frequency domain form, that is, Laplace transform is performed, as shown in the following formula:

[0064]

[0065] Wherein L represents inductance, C represents capacitance, and s is the Laplace operator, which has the same meaning as s in the above description.

[0066] The incremental equation is rearranged and transformed to derive the expressions of output voltage and output current respectively. The equivalent impedance of the device is calculated according to the following formula.

[0067]

[0068] △u is the micro increment of the device output voltage, △i is the micro increment of the device output current, and z represents the equivalent impedance of the device. The specific simplified circuit is as follows: Figure 2 As shown in Figure 1. z is also the transfer function expression of the device equivalent impedance, with the variable being the Laplace operator s. The Bode diagram of z is drawn using the software MATLAB.

[0069] The Bode diagram is divided into amplitude-frequency characteristic curve and phase-frequency characteristic curve.

[0070] The amplitude-frequency characteristic curve is the response of the impedance amplitude under frequency. The horizontal axis of the curve is the logarithm of the frequency, and the vertical axis is 20log|G|. The unit is decibel, "dB".

[0071] Where G is the transfer function expression.

[0072] The phase-frequency characteristic curve is the response of the impedance phase under frequency. The horizontal axis of the curve is the logarithm of the frequency, and the vertical axis is the phase, and the unit is degree.

[0073] Impedance is the composite of resistance and reactance, as shown in the following formula:

[0074]

[0075] In the formula, R is resistance, X is reactance, and Z is impedance. For phase.

[0076]

[0077] The Bode diagram of the impedance function is consistent with the above relationship, and the specific analysis is as follows:

[0078] Modify the Bode plot function information in MATLAB, change the horizontal axis from logarithmic coordinates to linear coordinates, change the unit from rad / s to Hz, change the vertical axis of the amplitude-frequency characteristic curve from "dB" to "abs", and its meaning changes from 20log|G| to |G|.

[0079] After the modification, the equivalent resistance and equivalent reactance of the system can be calculated based on the information of the Bode diagram. The specific operation is:

[0080]

[0081] Consistent with the decomposition method of impedance, the frequency-dependent curves of the equivalent resistance and equivalent reactance of the equipment can be obtained based on the Bode diagram of the impedance function.

[0082] This method makes full use of the physical properties of impedance, is more in line with its formation principle, and has clear and definite physical meaning.

[0083] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.

Claims

1. A method for obtaining an equivalent impedance of a device and an impedance-frequency characteristic curve, characterized in that: The method includes: Step 1: Establish an impedance network model of the target device, simplify the impedance network model using circuit principles and Laplace transform to obtain equivalent impedance; Step 2: Use MATLAB software to draw the Bode diagram of equivalent impedance; Step 3: Change the coordinates of the Bode diagram to linear coordinates, and use the Bode diagram in the linear coordinate system to find the equivalent resistance, equivalent reactance and impedance frequency curve of the target device.

2. A method for obtaining an equivalent impedance of a device and an impedance frequency characteristic curve according to claim 1, characterized in that: In step 1, the method for establishing the target device impedance network model is: The impedance network models of different devices of the target device are established, and the impedance network models of different devices are connected according to the topological structure relationship of the target device system to obtain the impedance network model of the target device.

3. The method for obtaining the equivalent impedance and impedance frequency characteristic curve of a device according to claim 1, characterized in that: In step 1, the impedance network model is simplified by using circuit principles and Laplace transform to obtain the equivalent impedance: The impedance network model is transformed into an incremental equation. In the incremental equation, the differential term is directly Laplace transformed: In the formula, A is the differential coefficient, B is the change, t is time, and s is the Laplace operator. The inductance and capacitance are Laplace transformed: Where L represents inductance and C represents capacitance. The original circuit is simplified to a simple RLC second-order circuit. The equivalent impedance is the ratio of the output voltage to the output current. Calculate the equivalent impedance of the device: △u is the micro increment of the device output voltage, △i is the micro increment of the device output current, and z represents the equivalent impedance of the device.

4. A method for obtaining an equipment equivalent impedance and an impedance frequency characteristic curve according to claim 3, characterized in that: In step 2, the Bode diagram expression of equivalent impedance is: In the formula, R is the equivalent resistance, X is the equivalent reactance, and Z is the equivalent impedance. For phase.

5. A method for obtaining the equivalent impedance of a device and the impedance frequency characteristic curve according to claim 4, characterized in that: In step 3, the method to change the coordinates of the Bode diagram to linear coordinates is: The frequency logarithm of the abscissa of the amplitude-frequency characteristic curve and the phase-frequency characteristic curve in the Bode diagram is changed to a linear coordinate, and the unit is changed from rad / s to Hz; the ordinate of the amplitude-frequency characteristic curve is changed from dB to abs.

6. A method for obtaining the equivalent impedance of a device and the impedance frequency characteristic curve according to claim 5, characterized in that: In step 3, the equivalent resistance and equivalent reactance of the target device are: Where ψ is the phase of the impedance in the actual circuit.

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