Filter capacitor state monitoring method without voltage sensor
Through the filtered capacitor state monitoring method of voltageless sensor, the capacitance voltage is reconstructed and estimated using an expansion state observer, which solves the problems of complex and low efficiency of the existing capacitor state monitoring method, and achieves high accuracy and flexibility monitoring effects.
Patent Information
- Application Number
- CN202411765742.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-03
- Publication Date
- 2025-03-14
AI Technical Summary
The existing capacitor status monitoring methods have problems such as complex operation, low monitoring efficiency, poor economics, and limited application scope. Especially in the fields of wind power converters, it is difficult to meet the needs of high precision and flexibility.
The filtering capacitance state monitoring method of voltageless sensor is adopted, and the capacitor voltage is reconstructed through the online monitoring method and sensor detection method, reducing the use of sensors, and designing an expansion state observer to estimate the capacitance voltage, thereby monitoring the capacitor status.
It improves the accuracy and efficiency of monitoring, reduces monitoring costs, simplifies the monitoring process, and is suitable for scenarios such as wind power converters that have been put into operation.
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Figure CN119619669A_ABST
Abstract
Description
[0001] Methodology Area
[0002] The invention relates to the technical field of power electronics, and in particular to a method for monitoring the state of a filter capacitor without a voltage sensor.
[0003] Background Methods
[0004] As voltage source converters are widely used as key equipment in modern power systems, they are increasingly used in uninterruptible power supply systems, photovoltaic power generation systems, wind power generation systems, and superconducting energy storage systems due to their low harmonic output, excellent output stability, high power capacity, low electromagnetic interference, and strong adaptability. These fields have extremely high requirements on the reliability of converters and the quality of grid-connected current. Therefore, it is particularly important to study the reliability of converters and optimize the quality of grid-connected current. The reliability of converters is not only closely related to the performance of power electronic devices, but also has an important relationship with the state of passive devices. Power electronic devices such as transistors and diodes may fail during high-frequency switching operations, and the aging and performance degradation of passive devices will also affect the overall operation of the converter.
[0005] Methods for capacitor condition monitoring have been extensively studied and can be divided into three categories: offline condition monitoring, quasi-online condition monitoring, and online condition monitoring. Offline condition monitoring usually requires disassembling the capacitor and using high-precision LCR meters or impedance analyzers to perform parameter tests to evaluate the condition of the capacitor. Quasi-online condition monitoring uses the converter to detect the condition of the capacitor in a specific operating mode, such as start-up, shutdown, or no-load mode. The online condition monitoring method collects the voltage and current of the capacitor by connecting auxiliary equipment or adjusting the control algorithm during the operation of the converter, and calculates the condition parameters through data analysis.
[0006] Although the offline status monitoring method has high accuracy, it is complicated to operate and has low monitoring efficiency. The required precision instruments are often expensive and have poor economic efficiency. The quasi-online status monitoring method has high monitoring accuracy and relatively simple operation characteristics, and is performed when the system is preparing or ending operation, so it will not interfere with normal operation. However, this method can only be implemented under specific working conditions, and the application conditions are relatively harsh, which limits the scope of application of this method. The online status monitoring method does not require the removal of capacitors and can be monitored while the equipment is running. It has high flexibility, but usually requires additional sensors or modified control algorithms, and the monitoring accuracy is relatively low. For wind power converters that have been put into operation, its applicability is also limited.
[0007] Therefore, a filter capacitor state monitoring method without a voltage sensor is provided to solve the above problems. Summary of the invention
[0008] The purpose of the present invention is to provide a method for monitoring the state of a filter capacitor without a voltage sensor. Based on the online monitoring method and the sensor detection method for monitoring the state of the capacitor, the capacitor voltage is reconstructed, the use of sensors is reduced, the capacitor voltage is estimated, and the estimated voltage is used to monitor the state of the capacitor, thereby reducing the use of voltage sensors and improving the monitoring accuracy.
[0009] To achieve the above object, the present invention provides a method for monitoring the state of a filter capacitor without a voltage sensor, comprising the following steps:
[0010] S1: Sampling the DC side voltage of the converter, obtaining the converter output voltage using the DC side voltage and the converter switch state, and obtaining the filter capacitor voltage using the converter output voltage and output current;
[0011] S2: Input the sampled current and the converter output voltage into the extended state observer, observe the intermediate variables, obtain the reconstructed capacitor voltage, and compare the waveform of the reconstructed capacitor voltage with the waveform of the actual voltage;
[0012] S3: Identify the transfer function of the reconstructed voltage by using identification technology, perform Bode analysis on the transfer function of the reconstructed voltage, select a frequency that meets the standard, and calculate the estimated capacitance parameters of the converter according to the selected frequency;
[0013] S4: Use an LCR analyzer to measure the converter data and obtain the actual capacitance parameters of the converter;
[0014] S5: Compare the estimated capacitance parameters with the actual capacitance parameters, perform error analysis, and make a life end judgment based on the life end judgment criteria.
[0015] Preferably, in step S1, the inverter switching state is set to an ideal state, and the corresponding switching function S x It is expressed as:
[0016]
[0017] Where x represents the phase of three-phase alternating current;
[0018] In the case of fundamental frequency, the switching function S x It is expressed as:
[0019]
[0020] Where S a represents the switching function of phase a, S b represents the b-phase switching function, S c represents the c-phase switching function, ω represents the angular frequency, and δ represents the time delay.
[0021] Preferably, in step S1, the DC side voltage of the converter is sampled, and the DC side voltage and the converter switch state are used to obtain the converter output voltage. The DC side output voltage u of the converter is 1d And the AC side output voltage u 1q Respectively expressed as:
[0022]
[0023] Among them, M d The average duty cycle of the d-axis obtained by the modulation wave information, M q Indicates the average duty cycle of the q-axis obtained by the modulation wave information, u dc Indicates the DC side power supply voltage.
[0024] Preferably, in step S1, the filter capacitor voltage is obtained using the converter output voltage and output current, which specifically includes the following steps:
[0025] S11: Write the KVL equation for the AC side system of the converter. The KVL equation is expressed as:
[0026]
[0027] where i a represents the a-phase current, i b represents the b-phase current, i c represents the c-phase current, u ca Indicates the voltage of phase a, u cb Indicates the voltage of phase b, u cc represents the phase c voltage, the voltage u at point O on the DC side relative to point n on the AC side on It is expressed as:
[0028]
[0029] S12: Get u according to the switching function on is 0, and the KVL equation of the converter system in the three-phase abc stationary coordinate system is obtained. The KVL equation is expressed as:
[0030]
[0031] Where R represents the equivalent series resistance on the AC side, and L1 represents the filter inductance on the AC side;
[0032] S13: Perform Park transformation on the KVL equation in step S21 to obtain the KVL equation of the converter system in the dq synchronous rotating coordinate system. The KVL equation is expressed as:
[0033]
[0034] where i drepresents the current of the d-axis, i q represents the current on the q axis, u cd represents the voltage of the d-axis, u cq Indicates the voltage of the q-axis.
[0035] Preferably, in step S2, the sampled current and the converter output voltage are input into an extended state observer, the intermediate variables are observed, the reconstructed capacitor voltage is obtained, and the waveform of the reconstructed capacitor voltage is compared with the waveform of the actual voltage, which specifically includes the following steps:
[0036] S21: According to the current state of the q axis, the expanded state variable x is obtained 2q , expressed as:
[0037] (-R1 / L)i q +ωi d -u cq / L1
[0038] Where R1 represents the equivalent parasitic resistance of AC side filtering;
[0039] S22: Get the parameter e of the extended state observer of the q axis 1q , e 1q It is expressed as:
[0040]
[0041] Where β1 and β2 represent the error gain coefficients, Z 1q is the current i on the q axis q The tracking parameter, Z 2q is the expanded state variable x 2q The tracking parameter, control gain b0 is expressed as:
[0042] b0=1 / L1;
[0043] S23: According to the extended state observer parameters of the q-axis, the voltage u of the q-axis is obtained cq ,u cq It is expressed as:
[0044]
[0045] S24: Get the transfer function u of the reconstructed voltage c ,u c It is expressed as:
[0046]
[0047] Where s represents the complex frequency, U1 represents the output voltage on the AC side, and I1 represents the output current on the AC side.
[0048] Preferably, in step S22, the characteristic equation λ(s) corresponding to the extended state observer is expressed as:
[0049] λ(s)=s 2 +β1s+β2
[0050] where λ(s) is set to (s+ω0) 2 , β1 is set to 2ω0, β2 is set to ω0 2 , ω0 represents the bandwidth of the extended state observer.
[0051] Preferably, in step S3, the transfer function of the reconstructed voltage is identified by an identification technique, and the reconstructed identification function is expressed as:
[0052]
[0053] Among them U c Indicates the filter capacitor voltage;
[0054] The transfer function of the actual voltage is identified through identification technology, and the actual identification function is expressed as:
[0055]
[0056] Preferably, in step S4, the converter data is measured using an LCR analyzer to obtain actual parameters of the filter capacitor.
[0057] Preferably, the capacitor voltage U cx With the capacitor current I cx The impedance relationship between them is expressed as:
[0058]
[0059] Where C represents the filter capacitor.
[0060] Therefore, the present invention adopts the above-mentioned filter capacitor state monitoring method without voltage sensor, which has the following beneficial effects:
[0061] (1) Adopt intelligent monitoring methods and combine data analysis technology to improve the intelligence level of monitoring and provide more accurate support for capacitor health management;
[0062] (2) The voltage reconstruction link is added to realize the reconstruction of capacitor voltage, reduce the use of sensors, reduce monitoring costs, and use simpler forms to solve more complex monitoring problems, greatly improving monitoring efficiency;
[0063] (3) An extended state observer is designed to estimate the capacitor voltage, and the estimated voltage is then used to monitor the state of the capacitor, eliminating the need for a voltage sensor and improving monitoring accuracy.
[0064] The method scheme of the present invention is further described in detail below through the drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS
[0065] Figure 1 A flow chart of a method for monitoring filter capacitor status without a voltage sensor according to the present invention;
[0066] Figure 2 This is a simplified diagram of the converter structure of the present invention;
[0067] Figure 3 A comparison diagram of the reconstructed voltage waveform and the actual voltage waveform of the present invention;
[0068] Figure 4 Bode diagrams of the actual transfer function and the reconstructed transfer function of the present invention;
[0069] Figure 5 This is the capacitor life termination criterion of the present invention. DETAILED DESCRIPTION
[0070] The method scheme of the present invention is further described below through drawings and embodiments.
[0071] Unless otherwise defined, method terms or scientific terms used in the present invention shall have the common meanings understood by one of ordinary skill in the art to which the present invention belongs.
[0072] The words "include" or "comprises" and the like used in the present invention mean that the elements before the word include the elements listed after the word, and do not exclude the possibility of also including other elements. The orientation or position relationship indicated by the terms "inside", "outside", "upper", "lower", etc. is based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it cannot be understood as a limitation of the present invention. When the absolute position of the described object changes, the relative position relationship may also change accordingly. In the present invention, unless otherwise clearly specified and limited, the terms "attachment" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral body; it can be directly connected, or indirectly connected through an intermediate medium, and it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.
[0073] Example
[0074] To simplify the calculation, this embodiment simplifies the commutation system into a single-phase form, such as Figure 2 As shown, u dcis the DC power supply voltage, u1 is the AC output voltage, u g is the grid side voltage, i cd is the output current of the converter DC side, C1 is the parallel capacitor on the converter DC side, R is the equivalent series resistance on the converter AC side, L is the equivalent inductance on the converter AC side, C is the filter capacitor, R c is the parasitic resistance of the filter capacitor, and the phases x are a, b, and c respectively, then u cx represents the voltage of phase x of the AC system, i x represents the current in phase x of the AC system, u 1x.n represents the voltage on the AC side x of the converter relative to the neutral point n of the AC system, u 1x.o It represents the voltage at the midpoint of the x-phase bridge arm on the AC side of the converter relative to the ground point o.
[0075] like Figure 1 As shown, the present invention provides a method for monitoring the state of a filter capacitor without a voltage sensor, comprising the following steps:
[0076] S1: Sampling the DC side voltage of the converter, obtaining the converter output voltage using the DC side voltage and the converter switch state, and obtaining the filter capacitor voltage using the converter output voltage and output current;
[0077] In step S1, the converter switching state is set to an ideal state, and the corresponding switching function S x It is expressed as:
[0078]
[0079] Where x represents the phase of three-phase alternating current;
[0080] In the case of fundamental frequency, the switching function S x It is expressed as:
[0081]
[0082] Where S a represents the switching function of phase a, S b represents the b-phase switching function, S c represents the c-phase switching function, ω represents the angular frequency, and δ represents the time delay;
[0083] In step S1, the DC side voltage of the converter is sampled, and the converter output voltage is obtained by using the DC side voltage and the converter switch state. The DC side output voltage u 1d And the AC side output voltage u 1q Respectively expressed as:
[0084]
[0085] Among them, M d The average duty cycle of the d-axis obtained by the modulation wave information, M q Indicates the average duty cycle of the q-axis obtained by the modulation wave information, u dc Indicates the DC side power supply voltage;
[0086] In step S1, the filter capacitor voltage is obtained using the converter output voltage and output current, which specifically includes the following steps:
[0087] S11: Write the KVL equation for the AC side system of the converter. The KVL equation is expressed as:
[0088]
[0089] where i a represents the a-phase current, i b represents the b-phase current, i c represents the c-phase current, u ca Indicates the voltage of phase a, u cb represents the voltage of phase b, u cc represents the phase c voltage, the voltage u at point O on the DC side relative to point n on the AC side on It is expressed as:
[0090]
[0091] S12: Get u according to the switching function on is 0, and the KVL equation of the converter system in the three-phase abc stationary coordinate system is obtained. The KVL equation is expressed as:
[0092]
[0093] Where R represents the equivalent series resistance on the AC side, and L1 represents the filter inductance on the AC side;
[0094] S13: Perform Park transformation on the KVL equation in step S21 to obtain the KVL equation of the converter system in the dq synchronous rotating coordinate system. The KVL equation is expressed as:
[0095]
[0096] where i d represents the current of the d-axis, i q represents the current on the q axis, u cd represents the voltage of the d-axis, u cq represents the voltage of the q-axis;
[0097] Through the transformation, the three-phase state equation is reduced to two-phase, and the AC quantity is converted into a DC quantity, which greatly simplifies the design of the controller.
[0098] S2: Input the sampled current and converter output voltage into the extended state observer, observe the intermediate variables, obtain the reconstructed capacitor voltage, and compare the waveform of the reconstructed capacitor voltage with the waveform of the actual voltage, such as Figure 3 As shown, the waveform of the reconstructed voltage is compared with the waveform of the actual voltage;
[0099] In step S2, the sampled current and the converter output voltage are input into the extended state observer, the intermediate variables are observed, the reconstructed capacitor voltage is obtained, and the waveform of the reconstructed capacitor voltage is compared with the waveform of the actual voltage, which specifically includes the following steps:
[0100] S21: According to the current state of the q axis, the expanded state variable x is obtained 2q , expressed as:
[0101] (-R1 / L)i q +ωi d -u cq / L1
[0102] Where R1 represents the parasitic equivalent resistance of the AC side filter;
[0103] S22: Get the parameter e of the extended state observer of the q axis 1q , e 1q It is expressed as:
[0104]
[0105] Where β1 and β2 represent the error gain coefficients, Z 1q is the current i on the q axis q The tracking parameter, Z 2q is the expanded state variable x 2q The tracking parameter, control gain b0 is expressed as:
[0106] b0=1 / L1;
[0107] In step S22, the characteristic equation λ(s) corresponding to the extended state observer is expressed as:
[0108] λ(s)=s 2 +β1s+β2
[0109] where λ(s) is set to (s+ω0) 2 , β1 is set to 2ω0, β2 is set to ω0 2 , ω0 represents the bandwidth of the extended state observer.
[0110] S23: According to the extended state observer parameters of the q-axis, the voltage u of the q-axis is obtained cq ,u cq It is expressed as:
[0111]
[0112] S24: Get the transfer function u of the reconstructed voltage c ,u c It is expressed as:
[0113]
[0114] Where s represents the complex frequency, U1 represents the output voltage on the AC side, and I1 represents the output current on the AC side.
[0115] S3: Figure 4 As shown, the transfer function of the reconstructed voltage is identified by identification technology, and the transfer function of the reconstructed voltage is subjected to Bode analysis. The Bode diagrams of the actual transfer function and the reconstructed transfer function are drawn. The waveforms of the reconstructed transfer function and the actual transfer function directly measured by the LCR analyzer are completely consistent before 1000rad / s, so the reconstructed voltage can replace the actual voltage.
[0116] A frequency that meets the standard is selected, and the estimated capacitance parameters of the converter are calculated according to the selected frequency. In this embodiment, the amplitude and phase at the reconstructed voltage frequencies of 50 Hz, 100 Hz, and 150 Hz are selected respectively;
[0117] Capacitor voltage U cx With the capacitor current I cx The impedance relationship between them is expressed as:
[0118]
[0119] Where C is the filter capacitor, the values of x are 50, 100 and 150, and the ω corresponding to x are 314, 628 and 942 respectively. The average value is 1.946e -5 , R is 1.945e -3 ;
[0120] Then the actual voltage amplitude and phase at frequencies of 50Hz, 100Hz, and 150Hz are directly measured by the LCR analyzer. In the actual capacitance-impedance relationship, C is 2e -5 , R is 2e -3 ;
[0121] The estimated capacitance parameters are offset by about 2.7% compared to the actual capacitance parameters.
[0122] In step S3, the transfer function of the reconstructed voltage is identified by an identification technique, and the reconstructed identification function is expressed as:
[0123]
[0124] Among them U cIndicates the filter capacitor voltage;
[0125] The transfer function of the actual voltage is identified through identification technology, and the actual identification function is expressed as:
[0126]
[0127] S4: Use an LCR analyzer to measure the converter data and obtain the actual capacitance parameters of the converter;
[0128] In step S4, the converter data is measured using an LCR analyzer to obtain actual parameters of the filter capacitor.
[0129] S5: Figure 5 As shown, the estimated capacitance parameters are compared with the actual capacitance parameters, an error analysis is performed, and the life end judgment is performed according to the life end judgment criteria.
[0130] Therefore, the present invention adopts the above-mentioned filter capacitor state monitoring method without voltage sensor, based on the online monitoring method and sensor detection method to monitor the capacitor state, adds a voltage reconstruction link, can realize the reconstruction of the capacitor voltage, reduces the use of sensors, designs an extended state observer to estimate the capacitor voltage, and then uses the estimated voltage to monitor the state of the capacitor, eliminating the use of voltage sensors and improving the monitoring accuracy.
[0131] Finally, it should be noted that the above embodiments are only used to illustrate the method scheme of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, ordinary method personnel in the field should understand that they can still modify or replace the method scheme of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified method scheme to deviate from the spirit and scope of the method scheme of the present invention.
Claims
1. A method for monitoring filter capacitor status without voltage sensor, characterized in that: The following steps are involved: S1: Sampling the DC side voltage of the converter, obtaining the converter output voltage using the DC side voltage and the converter switch state, and obtaining the filter capacitor voltage using the converter output voltage and output current; S2: Input the sampled current and the converter output voltage into the extended state observer, observe the intermediate variables, obtain the reconstructed capacitor voltage, and compare the waveform of the reconstructed capacitor voltage with the waveform of the actual voltage; S3: Identify the transfer function of the reconstructed voltage by using identification technology, perform Bode analysis on the transfer function of the reconstructed voltage, select a frequency that meets the standard, and calculate the estimated capacitance parameters of the converter according to the selected frequency; S4: Use an LCR analyzer to measure the converter data and obtain the actual capacitance parameters of the converter; S5: Compare the estimated capacitance parameters with the actual capacitance parameters, perform error analysis, and make a life end judgment based on the life end judgment criteria.
2. The method for monitoring filter capacitor status without voltage sensor according to claim 1, characterized in that: In step S1, the converter switching state is set to an ideal state, and the corresponding switching function S x It is expressed as: Where x represents the phase of three-phase alternating current; In the case of fundamental frequency, the switching function S x It is expressed as: Where S a represents the switching function of phase a, S b represents the b-phase switching function, S c represents the c-phase switching function, ω represents the angular frequency, and δ represents the time delay.
3. The method for monitoring filter capacitor status without voltage sensor according to claim 1, characterized in that: In step S1, the DC side voltage of the converter is sampled, and the converter output voltage is obtained by using the DC side voltage and the converter switch state. The DC side output voltage u 1d And the AC side output voltage u 1q Respectively expressed as: Among them, M d The average duty cycle of the d-axis obtained by the modulation wave information, M q Indicates the average duty cycle of the q-axis obtained by the modulation wave information, u dc Indicates the DC side power supply voltage.
4. The method for monitoring filter capacitor status without voltage sensor according to claim 1, characterized in that: In step S1, the filter capacitor voltage is obtained using the converter output voltage and output current, which specifically includes the following steps: S11: Write the KVL equation for the AC side system of the converter. The KVL equation is expressed as: where i a represents the a-phase current, i b represents the b-phase current, i c represents the c-phase current, u ca Indicates the voltage of phase a, u cb represents the voltage of phase b, u cc represents the phase c voltage, the voltage u at point O on the DC side relative to point n on the AC side on It is expressed as: S12: Get u according to the switching function on is 0, and the KVL equation of the converter system in the three-phase abc stationary coordinate system is obtained. The KVL equation is expressed as: Where R represents the equivalent series resistance on the AC side, and L1 represents the filter inductance on the AC side; S13: Perform Park transformation on the KVL equation in step S21 to obtain the KVL equation of the converter system in the dq synchronous rotating coordinate system. The KVL equation is expressed as: where i d represents the current of the d-axis, i q represents the current on the q axis, u cd represents the voltage of the d-axis, u cq Indicates the voltage of the q-axis.
5. The method for monitoring filter capacitor status without voltage sensor according to claim 1, characterized in that: In step S2, the sampled current and the converter output voltage are input into the extended state observer, the intermediate variables are observed, the reconstructed capacitor voltage is obtained, and the waveform of the reconstructed capacitor voltage is compared with the waveform of the actual voltage, which specifically includes the following steps: S21: According to the current state of the q axis, the expanded state variable x is obtained 2q , expressed as: (-R1 / L)i q +ωi d -u cq / L1 Where R1 represents the equivalent parasitic resistance of AC side filtering; S22: Get the parameter e of the extended state observer of the q axis 1q , e 1q It is expressed as: Where β1 and β2 represent the error gain coefficients, Z 1q is the current i on the q axis q The tracking parameter, Z 2q is the expanded state variable x 2q The tracking parameter, control gain b0 is expressed as: b0=1 / L1; S23: According to the extended state observer parameters of the q-axis, the voltage u of the q-axis is obtained cq ,u cq It is expressed as: u cq =-L1(z 2q +(R1 / L1)i q +ωi d ); S24: Get the transfer function u of the reconstructed voltage c ,u c It is expressed as: Where s represents the complex frequency, U1 represents the output voltage on the AC side, and I1 represents the output current on the AC side.
6. The method for monitoring filter capacitor status without voltage sensor according to claim 5, characterized in that: In step S22, the characteristic equation λ(s) corresponding to the extended state observer is expressed as: λ(s)=s 2 +β1s+β2 where λ(s) is set to (s+ω0) 2 , β1 is set to 2ω0, β2 is set to ω0 2 , ω0 represents the bandwidth of the extended state observer.
7. The method for monitoring filter capacitor status without voltage sensor according to claim 1, characterized in that: In step S3, the transfer function of the reconstructed voltage is identified by an identification technique, and the reconstructed identification function is expressed as: Among them U c Indicates the filter capacitor voltage; The transfer function of the actual voltage is identified through identification technology, and the actual identification function is expressed as:
8. The method for monitoring filter capacitor status without voltage sensor according to claim 1, characterized in that: In step S4, the converter data is measured using an LCR analyzer to obtain actual parameters of the filter capacitor.
9. The method for monitoring filter capacitor status without voltage sensor according to claim 1, characterized in that: Capacitor voltage U cx With the capacitor current I cx The impedance relationship between them is expressed as: Where C represents the filter capacitor.