WO2020119092A1 - 基于逆向卡尔曼滤波器的Buck变换器故障检测方法 - Google Patents

基于逆向卡尔曼滤波器的Buck变换器故障检测方法 Download PDF

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WO2020119092A1
WO2020119092A1 PCT/CN2019/094386 CN2019094386W WO2020119092A1 WO 2020119092 A1 WO2020119092 A1 WO 2020119092A1 CN 2019094386 W CN2019094386 W CN 2019094386W WO 2020119092 A1 WO2020119092 A1 WO 2020119092A1
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buck converter
time
matrix
estimated value
state
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French (fr)
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王子赟
王艳
刘子幸
纪志成
徐桂香
张帅
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Jiangnan University
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Jiangnan University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/40—Testing power supplies
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M3/00—Conversion of DC power input into DC power output
    • H02M3/02—Conversion of DC power input into DC power output without intermediate conversion into AC
    • H02M3/04—Conversion of DC power input into DC power output without intermediate conversion into AC by static converters
    • H02M3/10—Conversion of DC power input into DC power output without intermediate conversion into AC by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M3/145—Conversion of DC power input into DC power output without intermediate conversion into AC by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M3/155—Conversion of DC power input into DC power output without intermediate conversion into AC by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
    • H02M3/156—Conversion of DC power input into DC power output without intermediate conversion into AC by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators
    • H02M3/158—Conversion of DC power input into DC power output without intermediate conversion into AC by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators including plural semiconductor devices as final control devices for a single load
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
    • G01R31/64—Testing of capacitors
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
    • G01R31/72—Testing of electric windings
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/32—Means for protecting converters other than automatic disconnection

Definitions

  • the embodiments of the present invention relate to the field of power converter fault detection, and in particular to a Buck converter fault detection method based on an inverse Kalman filter.
  • power converter As an important device in the intermediate link of power system conversion, power converter can be used in power system, energy, automobile, agriculture and other fields. With the expansion of the application field of electronic technology, the converter will continue to play an important role in various fields.
  • the chopper circuit Due to the degradation of electrolytic capacitors, switch failures, solder joint failures, etc., the chopper circuit often fails. In order to ensure the safe operation of the power converter, the power converter needs to be detected.
  • Fault diagnosis methods can be divided into two categories: model-based and data-driven.
  • the data-driven fault diagnosis method needs to be based on sufficient and reliable historical data, but the data collection process is often affected by different noises, the quality of the collected data is not high, and the real-time fault diagnosis is not good; based on The fault diagnosis method of the model is applicable to the known model, and has low dependence on the data source, but the accuracy of the detection results of some faults is not high.
  • an embodiment of the present invention provides a Buck converter fault detection method based on an inverse Kalman filter.
  • the technical solution is as follows:
  • a method for fault detection of a Buck converter based on an inverse Kalman filter includes:
  • the parameter matrix of the Buck converter at time k is estimated according to the following formula, and the elements in the parameter matrix are determined according to the values of the elements in the Buck converter;
  • K(k) P(k
  • k-1) P(k-1
  • the estimated parameter matrix of the Buck converter at time k determine the estimated value of each element in the Buck converter
  • X(k) represents the parameter matrix of the Buck converter at time k
  • Y(k) represents the observation matrix of the Buck converter at time k
  • H(k) represents the state matrix of the Buck converter at time k
  • V(k) represents the Buck at time k
  • the observed noise sequence of the converter, W(k) represents the process noise sequence of the Buck converter at time k
  • V(k) and W(k) are independent of each other
  • k) represents the time k
  • K(k) represents the Kalman filter gain matrix at time k
  • ⁇ represents the noise driving matrix
  • I represents the identity matrix
  • k is an integer;
  • i L (k) represents the inductor current of the Buck converter at time k
  • u O (k) represents the output voltage of the Buck converter at time k
  • H(k) [i L (k-1) ⁇ I 2 u O (k-1) ⁇ I 2 S(k) ⁇ I 2 ], I 2 represents a two-dimensional identity matrix, and S(k) represents a Buck transform The switching state of the MOSFET in the device;
  • T represents the sampling period
  • E represents the input voltage of the Buck converter
  • R represents the value of the resistance in the Buck converter
  • L represents the value of the inductance in the Buck converter
  • the electrolytic capacitor in the Buck converter is equivalent to the capacitance and series resistance
  • C represents The value of the capacitor
  • R C represents the value of the series resistance.
  • determine whether the Buck converter has failed including:
  • the predetermined time range is 1 to N, N is an integer, and 1 ⁇ k ⁇ N;
  • the estimated value of each element in the Buck converter is determined, including:
  • the state equation and the observation equation of the Buck converter are obtained according to the discrete model of the hybrid system, and the input voltage of the Buck converter during operation, the switching state of the switch, and the inductance are obtained.
  • the values of current and output voltage are used to determine the state matrix of the Buck converter according to the obtained values, and the parameter matrix of Buck at each moment is estimated recursively according to the state matrix, state equation, and observation matrix within a predetermined time range, and the estimated parameters
  • Each element in the matrix determines the estimated value of each component in the Buck converter, and detects whether the Buck converter is faulty in real time according to the estimated value of the component; it solves the problem that the current fault diagnosis of the Buck converter is not real-time and the accuracy is not high; The effect of improving the real-time and accuracy of the fault detection of the Buck converter is achieved.
  • the fault value when the component fails can be obtained, which has the characteristics of high reliability and strong followability.
  • Fig. 1 is a flowchart of a converter fault detection method based on an inverse Kalman filter according to an exemplary embodiment
  • FIG. 2 is a topology diagram of a Buck converter
  • Figure 3 is a schematic diagram of the topology of a non-ideal Buck converter
  • Fig. 4 is a graph showing a parameter change corresponding to an inductance L in a Buck converter according to an exemplary embodiment
  • Fig. 5 is a graph showing a parameter change corresponding to a resistance R in a Buck converter according to an exemplary embodiment
  • Fig. 6 is a graph showing a parameter change corresponding to a series resistance R C in a Buck converter according to an exemplary embodiment
  • Fig. 7 is a graph showing a parameter change corresponding to a capacitor C in a Buck converter according to an exemplary embodiment.
  • FIG. 1 shows a flowchart of a Buck converter fault detection method based on an inverse Kalman filter provided by an embodiment.
  • the Buck converter fault detection method based on the inverse Kalman filter may include the following steps:
  • Step 101 Establish a discrete model of the hybrid system of the non-ideal Buck converter under the condition that the inductor current continues to conduct.
  • the topology of the Buck converter is shown in Figure 2.
  • the Buck converter circuit is simplified by the equivalent conversion method of the non-ideal Buck converter, that is, the switch MOSFET is equivalent to the ideal switch S1, and the diode D is equivalent to the ideal switch.
  • S2 the inductance L is regarded as an ideal component, and the electrolytic capacitor C'is equivalent to the capacitor C and the series resistance R C.
  • the topology schematic diagram of the obtained non-ideal converter is shown in FIG. 3.
  • the Buck converter has two cases when the inductor current is continuously conducted (Continuous Conduction Mode, CCM mode): S1 is closed and S2 is turned on, and S1 is turned on and S2 is turned on, combining the states in the two cases to obtain the Buck in CCM mode Inverter hybrid system model:
  • S represents the switching state of the switch of the Buck converter
  • E represents the input voltage of the Buck converter
  • i L represents the inductor current of the Buck converter
  • u o represents the output voltage of the Buck converter
  • the components of the Buck converter include an inductance L, a resistance R, an electrolytic capacitor C', a capacitor C equivalent to a series resistance R C.
  • T represents the sampling period
  • k is the discrete time
  • i L (k) represents the inductance current of the Buck converter at time k
  • u O (k) represents the output voltage of the Buck converter at time k
  • S(k) represents The switching state of the MOSFET in the Buck converter.
  • the value of S(k) is 1 or 0.
  • the value of S(k) is 1, it means that the MOSFET is in the on state, and the value of S(k) is 0 indicates that the MOSFET is off.
  • Step 102 Obtain the state equation and observation equation of the Buck converter according to the discrete model of the hybrid system.
  • I 2 represents a two-dimensional identity matrix
  • the element of the observation matrix Y(k) is the inductor current i L (k) and output voltage u O (k) can be obtained by measuring the Buck circuit.
  • the estimated value of the unknown state of the system is obtained according to the known parameters of the system; in the embodiment of the present invention, the reverse Kalman filter algorithm is used, that is, the unknown state of the system is obtained according to the known state of the system.
  • the estimated value of the parameter of, that is, the unknown parameter matrix X(k) is obtained according to the known state matrix H(k).
  • the unknown parameter matrix X(k) of the Buck converter is converted into a state matrix form
  • the known state matrix H(k) of the Buck converter is converted into a parameter matrix form, namely:
  • w i (k) is the process noise sequence of the Buck converter, and is a Gaussian white noise sequence with an average value of zero.
  • the state equation of the Buck converter can be determined:
  • W(k) is the process noise sequence of the Buck converter at time k
  • Q k is the variance matrix of the process noise sequence W(k)
  • ⁇ ki is the Kronic delta function.
  • V(k) represents the observation noise sequence of the Buck converter at time k, and V(k) and W(k) are independent of each other.
  • Step 103 Obtain the input voltage, switching state, inductor current, and output voltage of the Buck converter in the working state, and determine the state matrix of the Buck converter.
  • the predetermined time range is 1 to N, N is an integer, and the value of N is set in advance.
  • a Buck converter with unknown parameters use a voltmeter measurement and an oscilloscope to obtain the input voltage E, the switching state S of the switch, the inductor current i L, and the output voltage u O to obtain the state of the Buck converter
  • Step 104 According to the state matrix, the state equation and the observation equation, estimate the parameter matrix of the Buck converter at time k.
  • the parameter matrix of the Buck converter at time k is estimated based on the state matrix, state equations, and observation equations; the predetermined time range is 1 to N, N is an integer, and the value of N is preset; that is, k The value ranges from 1 to N.
  • the state matrix H(k) at time k can be determined by step 103.
  • the predicted covariance matrix P needs to be initialized.
  • the parameter matrix X(k) of the Buck converter at time k is estimated.
  • Equation (14) Calculate the innovation matrix ⁇ (k) at time k, which is Equation (14); innovation represents the difference between the predicted value and the measured value;
  • the parameter matrix X(k) of the Buck converter estimated at time k is which is
  • Step 105 Determine the estimated value of each element in the Buck converter according to the estimated parameter matrix of the Buck converter at time k.
  • the estimated value of each element in the Buck converter can be determined according to the elements in the parameter matrix.
  • Step 106 According to the estimated value of each element in the Buck converter, determine whether the Buck converter has failed.
  • the estimated value it can be determined in real time which element in the Buck converter has failed, and the parameter value when the element has failed can be determined.
  • the predetermined range is preset, and the predetermined range is determined according to actual needs.
  • the predetermined time range is 1 to N, N is an integer, and 1 ⁇ k ⁇ N.
  • the estimated value at each moment in the predetermined time range is compared with the reference value, and it is detected whether the difference between the estimated value and the reference value is within the predetermined range.
  • the stable estimated value finally obtained within a predetermined time range is determined as the fault value of the faulty component.
  • the component parameter change curve is drawn according to the estimated value of the component, that is, the component parameters are plotted for the series resistance and capacitance obtained by the equivalent of inductance, resistance, and electrolytic capacitor, respectively Curve.
  • the component parameter change curve you can intuitively see the estimated value of the component at each moment. According to the fluctuation and transition state of the component parameter change curve, you can intuitively see which component has failed. After the jump occurs from the component parameter change curve The final stable value of can get the fault value of the faulty component.
  • the embodiment of the present application obtains the state equation and the observation equation of the Buck converter according to the discrete model of the hybrid system by establishing the discrete model of the hybrid system of the non-ideal Buck converter in the working state, and obtains the Input voltage, the switching state of the switch, the inductor current and the output voltage, determine the state matrix of the Buck converter according to the obtained value, and estimate the parameters of Buck at various times according to the state matrix, state equation, and observation matrix within a predetermined time range Matrix, determine the estimated value of each component in the Buck converter according to each element in the estimated parameter matrix, and detect whether the Buck converter is faulty in real time according to the estimated value of the component; solves the current fault diagnosis of the Buck converter is not good in real time , The problem of low accuracy; to achieve the effect of improving the real-time performance and accuracy of Buck converter fault detection.
  • step 104 iteratively calculate k within a predetermined time range
  • the formula of the parameter matrix X(k) of the Buck converter at the moment is:
  • K(k) P(k
  • the forgetting factor is 0 ⁇ 1.
  • step 104 the formula for iteratively calculating the parameter matrix X(k) of the Buck converter at time k is Equations (11)-(16).
  • the forgetting factor ⁇ 0.9989, within the predetermined time range, after performing steps 101 to 106, the estimated values at various times within the predetermined time range are obtained, and the inductance L, resistance R, The capacitor C has not failed, and the series resistance R C has failed; according to the estimated value of each component, the parameter change curves of the inductance L, resistance R, series resistance R C and capacitor C in the Buck converter are drawn, as shown in Figure 4 and Figure 5 respectively Figure 6 and Figure 7; from Figure 7, it can be seen that the parameter change curve corresponding to the faulty series resistance R C fluctuates significantly and the value continues to rise within a certain period of time.
  • the fault detection method of the Buck converter based on the inverse Kalman filter detects whether the Buck converter is faulty when the Buck converter is in the working state, and it is assumed that the Buck converter Only a single component fails at the same time.
  • the program may be stored in a computer-readable storage medium.
  • the mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, etc.

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Abstract

本发明公开了一种基于逆向卡尔曼滤波器的Buck变换器故障检测方法，属于电力变换器故障检测领域。该方法包括建立非理想Buck变换器在电感电流持续导通情况下的混杂系统离散模型；获取Buck变换器的状态方程和观测方程；获取在工作状态下的输入电压、切换状态、电感电流和输出电压，确定Buck变换器的状态矩阵；根据状态矩阵、状态方程和观测方程，估计k时刻的参数矩阵；根据估计得到的k时刻Buck变换器的参数矩阵，确定各个元件的估计值；根据各个元件的估计值判断Buck变换器是否发生故障；解决了目前Buck变换器的故障诊断实时性不好，精度不高的问题；达到了提高Buck变换器故障检测的实时性和准确度的效果。

Description

基于逆向卡尔曼滤波器的Buck变换器故障检测方法 技术领域
本发明实施例涉及电力变换器故障检测领域，特别涉及一种基于逆向卡尔曼滤波器的Buck变换器故障检测方法。
背景技术
电力变换器作为电力系统转换中间环节的重要器件，可用于电力系统、能源、汽车、农业等领域。随着电子技术应用领域的拓展，变换器必将继续在各个领域发挥重要的作用。
由于电解电容退化、开关管故障、焊点故障等原因，常常导致斩波电路出现故障，为了保障电力变换器安全工作，需要对电力变换器进行故障检测。
故障诊断方法可以分为两大类：基于模型的和基于数据驱动的。其中，基于数据驱动的故障诊断方法需要以充足可靠的历史数据为前提，但数据采集过程中往往会受到不同噪声的影响，采集到的数据质量不高，且故障诊断的实时性不好；基于模型的故障诊断方法适用于已知的模型，对数据源的依赖性较低，但对某些故障的检测结果精度不高。
发明内容
为了解决现有技术的问题，本发明实施例提供了一种基于逆向卡尔曼滤波器的Buck变换器故障检测方法。该技术方案如下：
第一方面，提供了一种基于逆向卡尔曼滤波器的Buck变换器故障检测方法，该方法包括：
建立非理想Buck变换器在电感电流持续导通情况下的混杂系统离散模型；
根据混杂系统离散模型，获取Buck变换器的状态方程和观测方程；
获取Buck变换器在工作状态下的输入电压、切换状态、电感电流和输出电压，并确定Buck变换器的状态矩阵；
根据状态矩阵、状态方程和观测方程，按如下公式估计k时刻Buck变换器 的参数矩阵，参数矩阵中的元素根据Buck变换器中元件的值确定；
Figure PCTCN2019094386-appb-000001
Figure PCTCN2019094386-appb-000002
K(k)＝P(k|k-1)H T(k)·[H(k)P(k|k-1)H T(k)+R] -1；
P(k|k-1)＝P(k-1|k-1)/λ+ΓQ k-1Γ T；
Figure PCTCN2019094386-appb-000003
P(k|k)＝[I-K(k)H(k)]P(k|k-1)；
根据估计得到的k时刻Buck变换器的参数矩阵，确定Buck变换器中各个元件的估计值；
根据Buck变换器中各个元件的估计值判断Buck变换器是否发生故障；
其中，状态方程为X(k+1)＝X(k)+W(k)，观测方程为Y(k)＝H(k)X(k)+V(k)；
X(k)表示k时刻Buck变换器的参数矩阵，Y(k)表示k时刻Buck变换器的观测矩阵，H(k)表示k时刻Buck变换器的状态矩阵，V(k)表示k时刻Buck变换器的观测噪声序列，W(k)表示k时刻Buck变换器的过程噪声序列，V(k)与W(k)相互独立；
Figure PCTCN2019094386-appb-000004
表示k时刻参数矩阵X(k)的最优估计结果，
Figure PCTCN2019094386-appb-000005
表示利用
Figure PCTCN2019094386-appb-000006
进行估计得到的结果，P(k|k)表示k时刻
Figure PCTCN2019094386-appb-000007
对应的协方差矩阵，K(k)表示k时刻的卡尔曼滤波增益矩阵，Γ表示噪声驱动矩阵，I表示单位矩阵；λ表示遗忘因子，λ＝1或0＜λ＜1；k为整数；
Figure PCTCN2019094386-appb-000008
i L(k)表示k时刻Buck变换器的电感电流，u O(k)表示k时刻Buck变换器的输出电压；
H(k)＝[i L(k-1)·I 2 u O(k-1)·I 2 S(k)·I 2]，I 2表示二维单位矩阵，S(k)表示Buck变换器中MOSFET管的切换状态；
Figure PCTCN2019094386-appb-000009
T表示采样周期，E表示Buck变换器的输入电压，R表示Buck变换器中电阻的值，L表示Buck变换器中电感的值，Buck变换器中电解电容等效为电容和串联电阻，C表示电容的值，R C表示串联电阻的值。
可选的，根据Buck变换器中各个元件的估计值判断Buck变换器是否发生 故障，包括：
检测k时刻的估计值与参考值之差是否在预定范围内；预定时间范围为1至N，N为整数，1≤k≤N；
若检测到k时刻的估计值与参考值之差在预定范围内，则确定所述元件无故障；
若检测到k时刻的估计值与参考值之差在预定范围外，则检测k+1时刻至k+j时刻的估计值与参考值之差在预定范围外的数量是否为j；j为整数；
若检测到k+1时刻至k+j时刻的估计值与参考值之差在预定范围外的数量为j，则确定所述元件发生故障；
若检测到k+1时刻至k+j时刻的估计值与参考值之差在预定范围外的数量不为j，则确定所述元件无故障。
可选的，根据估计得到的k时刻Buck变换器的参数矩阵，确定Buck变换器中各个元件的估计值，包括：
按如下公式确定k时刻Buck变换器中电感的估计值：
Figure PCTCN2019094386-appb-000010
按如下公式确定k时刻Buck变换器中电阻的估计值：
Figure PCTCN2019094386-appb-000011
按如下公式确定k时刻Buck变换器中用于等效电解电容的串联电阻和电容的估计值：
Figure PCTCN2019094386-appb-000012
Figure PCTCN2019094386-appb-000013
本申请实施例提供的技术方案带来的有益效果是：
通过建立非理想Buck变换器在工作状态下的混杂系统离散模型，根据混杂系统离散模型获取Buck变换器的状态方程和观测方程，获取Buck变换器在工作时的输入电压、开关的切换状态、电感电流和输出电压的数值，根据获取到的数值确定Buck变换器的状态矩阵，在预定时间范围内根据状态矩阵、状态方程、观测矩阵递推估计Buck在各个时刻的参数矩阵，根据估计得到的参数矩阵 中的各个元素确定Buck变换器中各个元件的估计值，根据元件的估计值实时检测Buck变换器是否发生故障；解决了目前Buck变换器的故障诊断实时性不好，精度不高的问题；达到了提高Buck变换器故障检测的实时性和准确度的效果。
此外，还可以得到在元件发生故障时的故障数值，具有可靠性高、跟随性强的特点。
附图说明
为了更清楚地说明本申请实施例中的技术方案，下面将对实施例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申请的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。
图1是根据一示例性实施例示出的一种基于逆向卡尔曼滤波器的变换器故障检测方法的流程图；
图2是一种Buck变换器的拓扑图；
图3是一种非理想Buck变换器的拓扑原理图；
图4是根据一示例性实施例示出的一种Buck变换器中电感L对应的参数变化曲线图；
图5是根据一示例性实施例示出的一种Buck变换器中电阻R对应的参数变化曲线图；
图6是根据一示例性实施例示出的一种Buck变换器中串联电阻R C对应的参数变化曲线图；
图7是根据一示例性实施例示出的一种Buck变换器中电容C对应的参数变化曲线图。
具体实施方式
为使本申请的目的、技术方案和优点更加清楚，下面将结合附图对本申请实施方式作进一步地详细描述。
请参考图1，其示出了一个实施例提供的基于逆向卡尔曼滤波器的Buck变换器故障检测方法的流程图。如图1所示，该基于逆向卡尔曼滤波器的Buck 变换器故障检测方法可以包括以下步骤：
步骤101，建立非理想Buck变换器在电感电流持续导通情况下的混杂系统离散模型。
Buck变换器的拓扑图如图2所示，采用非理想Buck变换器等效变换的方法对Buck变换器电路进行简化，即将开关管MOSFET等效为理想开关S1，将二极管D等效为理想开关S2，将电感L视为理想元件，电解电容C＇等效为电容C和串联电阻R C，得到的非理想变换器的拓扑原理图如图3所示。
1、建立非理想Buck变换器的混杂系统模型。
由于Buck变换器在电感电流连续导通(Continuous Conduction Mode，CCM模式)时存在两种情况：S1闭合且S2开通、S1开通S2闭合，将两种情况下的状态结合，得到在CCM模式下Buck变换器的混杂系统模型：
Figure PCTCN2019094386-appb-000014
式(1)中S表示Buck变换器的开关管的切换状态，E表示Buck变换器的输入电压，i L表示Buck变换器的电感电流，u o表示Buck变换器的输出电压，
Figure PCTCN2019094386-appb-000015
表示i L关于时间t的一阶导数，
Figure PCTCN2019094386-appb-000016
表示u o关于时间t的一阶导数。
如图3所示，Buck变换器的元件包括电感L、电阻R、电解电容C＇等效得到的电容C和串联电阻R C。
2、对式(1)进行离散化处理，得到非理想Buck变换器在电感电流持续导通情况下的混杂系统离散模型：
Figure PCTCN2019094386-appb-000017
式(2)中T表示采样周期，k为离散时间，i L(k)表示k时刻Buck变换器的电感电流，u O(k)表示k时刻Buck变换器的输出电压；S(k)表示Buck变换器中MOSFET管的切换状态，在一个周期T内S(k)的值为1或0，S(k)的值为1时表示MOSFET管处于导通状态，S(k)的值为0时表示MOSFET管处于断开状态。
步骤102，根据混杂系统离散模型，获取Buck变换器的状态方程和观测方 程。
根据混杂系统离散模型，即式(2)，定义k时刻Buck变换器的状态矩阵H(k)、k时刻Buck变换器的参数矩阵X(k)、k时刻Buck变换器的观测矩阵Y(k)：
Figure PCTCN2019094386-appb-000018
Figure PCTCN2019094386-appb-000019
根据式(2)、(3)、(4)、(5)可得：
Y(k)＝H(k)X(k)      (6)
其中，I 2表示二维单位矩阵；未知的参数矩阵X(k)有6个元素x 1i(k)，i＝1，2，……，6；观测矩阵Y(k)的元素即电感电流i L(k)和输出电压u O(k)可以通过对Buck电路进行测量获得。
由式(4)可以看出，参数矩阵X(k)中的元素根据Buck变换器中元件的值确定。需要说明的是，带有“^”的参数表示估计值。
在卡尔曼滤波算法中，根据系统中已知的参数，得到的系统未知的状态的估计值；在本发明实施例中利用逆向卡尔曼滤波算法，即根据系统已知的状态，得到系统中未知的参数的估计值，也即根据已知的状态矩阵H(k)得到未知的参数矩阵X(k)。
根据式(6)，将Buck变换器的未知的参数矩阵X(k)转换为状态矩阵的形式，将Buck变换器的已知的状态矩阵H(k)转换为参数矩阵的形式，即：
令k时刻Buck变换器的参数x i(k)为：
x i(k)＝x 1i(k)       (7)
令k+1时刻Buck变换器的参数x i(k+1)为：
x i(k+1)＝x 1i(k)+w i(k)      (8)
其中，w i(k)是Buck变换器的过程噪声序列，是均值为零的高斯白噪声序列。
根据式(8)可以确定Buck变换器的状态方程：
X(k+1)＝X(k)+W(k)       (9)
其中，W(k)是k时刻Buck变换器的过程噪声序列，W(k)由w i(k)组成， 且E[W(k)W T(i)]＝Q kδ ki；Q k为非负定方差阵，Q k是过程噪声序列W(k)的方差矩阵，δ ki是克罗尼克δ函数。
根据式(6)可以确定Buck变换器的观测方程：
Y(k)＝H(k)X(k)+V(k)      (10)
V(k)表示k时刻Buck变换器的观测噪声序列，V(k)与W(k)相互独立。
步骤103，获取Buck变换器在工作状态下的输入电压、切换状态、电感电流和输出电压，并确定Buck变换器的状态矩阵。
在预定时间范围内，获取Buck变换器在工作状态下的输入电压、开关的切换状态、电感电流和输出电压。
预定时间范围为1至N，N为整数，N的值是预先设置的。
可选的，在未知参数的Buck变换器中，利用电压表测量和示波器采样，得到输入电压E、开关的切换状态S、电感电流i L和输出电压u O，得到Buck变换器的状态
再根据式(3)确定出Buck变换器的状态矩阵H(k)；k的取值范围为1至N，k为整数。
步骤104，根据状态矩阵、状态方程和观测方程，估计k时刻Buck变换器的参数矩阵。
在预定时间范围内，根据状态矩阵、状态方程和观测方程，估计k时刻Buck变换器的参数矩阵；预定时间范围为1至N，N为整数，N的值是预先设置的；即，k的取值范围为1至N。
在预定时间范围内，k时刻的状态矩阵H(k)均可以通过步骤103确定。
在估计Buck变换器的参数矩阵之前，需要对预测的协方差矩阵P进行初始化。
按式(11)-(16)递推计算，估计k时刻Buck变换器的参数矩阵X(k)。
Figure PCTCN2019094386-appb-000020
Figure PCTCN2019094386-appb-000021
K(k)＝P(k|k-1)H T(k)·[H(k)P(k|k-1)H T(k)+R] -1  (13)
Figure PCTCN2019094386-appb-000022
P(k|k-1)＝P(k-1|k-1)/λ+ΓQ k-1Γ T  (15)
P(k|k)＝[I-K(k)H(k)]P(k|k-1)      (16)
其中，
Figure PCTCN2019094386-appb-000023
表示k时刻参数矩阵X(k)的最优估计结果，
Figure PCTCN2019094386-appb-000024
表示利用
Figure PCTCN2019094386-appb-000025
进行估计得到的结果，P(k|k)表示k时刻
Figure PCTCN2019094386-appb-000026
对应的协方差矩阵，K(k)表示k时刻的卡尔曼滤波增益矩阵，I表示单位矩阵；Q k-1是过程噪声序列W(k-1)的方差矩阵；Γ表示噪声驱动矩阵，在此Buck变换器系统中Γ为单位矩阵。
式(15)中λ表示遗忘因子，λ＝1或0＜λ＜1。
由于历史数据会对故障检测的结果造成一定影响，若需要减小历史数据对检测结果的影响，则令0＜λ＜1；若不需要减小历史数据对检测结果的影响，则令λ＝1。
对参数矩阵估计的递推过程为：
(1)利用k-1时刻的参数矩阵X的最优估计结果
Figure PCTCN2019094386-appb-000027
进行预测，得到k时刻参数矩阵X的预测结果
Figure PCTCN2019094386-appb-000028
即式(12)；
(2)利用k-1时刻的
Figure PCTCN2019094386-appb-000029
对应的协方差矩阵P(k-1|k-1)，对k时刻的协方差矩阵P(k|k-1)进行预测，即式(15)；
(3)计算k时刻的卡尔曼滤波增益矩阵K(k)，即式(13)；
(4)计算k时刻的新息矩阵ε(k)，即式(14)；新息表示预测值与实测值之差；
(5)利用k时刻参数矩阵X的预测结果
Figure PCTCN2019094386-appb-000030
更新得到k时刻参数矩阵X的最优估计结果
Figure PCTCN2019094386-appb-000031
即式(11)；
(6)更新得到k时刻的
Figure PCTCN2019094386-appb-000032
对应的协方差矩阵P(k|k)，即式(16)。
估计得到的k时刻Buck变换器的参数矩阵X(k)是
Figure PCTCN2019094386-appb-000033
即
Figure PCTCN2019094386-appb-000034
步骤105，根据估计得到的k时刻Buck变换器的参数矩阵，确定Buck变换器中各个元件的估计值。
由于
Figure PCTCN2019094386-appb-000035
即
Figure PCTCN2019094386-appb-000036
Figure PCTCN2019094386-appb-000037
所以可以根据参数矩阵中的元素确定出Buck变换器中各个元件的估计值。
具体地：
按式(17)确定k时刻Buck变换器中电感的估计值
Figure PCTCN2019094386-appb-000038
Figure PCTCN2019094386-appb-000039
按式(18)确定k时刻Buck变换器中电阻的估计值
Figure PCTCN2019094386-appb-000040
Figure PCTCN2019094386-appb-000041
按式(19)和(20)确定k时刻Buck变换器中用于等效电解电容的串联电阻和电容的估计值，即
Figure PCTCN2019094386-appb-000042
和
Figure PCTCN2019094386-appb-000043
Figure PCTCN2019094386-appb-000044
Figure PCTCN2019094386-appb-000045
步骤106，根据Buck变换器中各个元件的估计值判断Buck变换器是否发生故障。
根据估计值可以实时确定Buck变换器中的哪个元件发生了故障，确定元件发生故障时的参数值。
在进行故障诊断之前，每个元件的参考值已知。
在预定时间范围内，针对Buck变换器中每个元件，检测k时刻的估计值与参考值之差是否在预定范围内。
可选的，预定范围是预先设置的，预定范围根据实际需要确定。
预定时间范围为1至N，N为整数，1≤k≤N。预定时间范围内的每个时刻的估计值均与参考值比较，并检测估计值与参考值之差是否在预定范围内。
若检测到k时刻的估计值与参考值之差在预定范围内，则确定元件无故障。
若检测到k时刻的估计值与参考值之差在预定范围外，则检测k+1时刻至k+j时刻的估计值与参考值之差在预定范围外的数量是否为j；j为整数。
依次检测k+1时刻的估计值与参考值之差是否在预定范围内，k+2时刻的估计值与参考值之差是否在预定范围内，k+3时刻的估计值与参考值之差是否在预定范围内，……，k+j时刻的估计值与参考值之差是否在预定范围内；检测估计值与参考值之差在预定范围外的数量是否为j。
若检测到k+1时刻至k+j时刻的估计值与参考值之差在预定范围外的数量为j，则确定元件故障。
若检测到检测k+1时刻至k+j时刻的估计值与参考值之差在预定范围外的数量不为j，则确定元件无故障。
j的值是预先设置的，j的值根据实际需要确定，比如j＝5。
在确定元件发生故障后，将在预定时间范围内最终得到的稳定的估计值确定为故障元件的故障值。
可选的，在预定时间范围内，针对Buck变换器中每个元件，根据元件的估计值绘制元件参数变化曲线，即针对电感、电阻、电解电容等效得到的串联电阻和电容分别绘制元件参数变化曲线。
根据元件参数变化曲线可以直观地看出元件在各个时刻的估计值，根据元件参数变化曲线的波动和跳变状态可以直观地看出哪个元件发生了故障，从元件参数变化曲线上发生跳变后的最终稳定值可以得到故障元件的故障数值。
综上所述，本申请实施例通过建立非理想Buck变换器在工作状态下的混杂系统离散模型，根据混杂系统离散模型获取Buck变换器的状态方程和观测方程，获取Buck变换器在工作时的输入电压、开关的切换状态、电感电流和输出电压的数值，根据获取到的数值确定Buck变换器的状态矩阵，在预定时间范围内根据状态矩阵、状态方程、观测矩阵估计Buck在各个时刻的参数矩阵，根据估计得到的参数矩阵中的各个元素确定Buck变换器中各个元件的估计值，根据元件的估计值实时检测Buck变换器是否发生故障；解决了目前Buck变换器的故障诊断实时性不好，精度不高的问题；达到了提高Buck变换器故障检测的实时性和准确度的效果。
此外，还可以确定在元件发生故障时确定故障数值，具有可靠性高、跟随性强的特点。
需要说明的是，本申请实施例中带有“^”的参数表示估计值。
在基于图1所示实施例的可选实施例中，若不考虑历史数据对元件参数估计的影响，则令遗忘因子λ＝1，在执行步骤104时，在预定时间范围内，迭代计算k时刻Buck变换器的参数矩阵X(k)的公式为：
Figure PCTCN2019094386-appb-000046
Figure PCTCN2019094386-appb-000047
K(k)＝P(k|k-1)H T(k)·[H(k)P(k|k-1)H T(k)+R] -1
Figure PCTCN2019094386-appb-000048
P(k|k-1)＝P(k-1|k-1)+ΓQ k-1Γ T
P(k|k)＝[I-K(k)H(k)]P(k|k-1)
在基于图1所示实施例的可选实施例中，若考虑历史数据对元件参数估计的影响，令故障检测的结果更准确，则令遗忘因子0＜λ＜1，在执行步骤104时，在预定时间范围内，迭代计算k时刻Buck变换器的参数矩阵X(k)的公式为式(11)-(16)。
遗忘因子λ是根据实际需要人为预先设置的；可选的，遗忘因子λ的取值在0.95～1之间，比如λ＝0.9989。
在一个例子中，令遗忘因子λ＝0.9989，在预定时间范围内，执行步骤101至步骤106后，得到在预定时间范围内各个时刻的估计值，确定出Buck变换器中电感L、电阻R、电容C没有发生故障，串联电阻R C出现故障；根据各个元件的估计值绘制Buck变换器中电感L、电阻R、串联电阻R C和电容C对应的参数变化曲线，分别如图4、图5、图6、图7所示；从图7可以看出，发生故障的串联电阻R C对应的参数变化曲线上有明显波动且在一定时间内数值持续上升。
需要说明的是，本申请实施例提供的基于逆向卡尔曼滤波器的Buck变换器的故障检测方法，检测Buck变换器是否发生故障是在Buck变换器处于工作状态下进行的，且假定Buck变换器在同一时刻只有单个元件发生故障。
需要说明的是：上述本申请实施例序号仅仅为了描述，不代表实施例的优劣。
本领域普通技术人员可以理解实现上述实施例的全部或部分步骤可以通过硬件来完成，也可以通过程序来指令相关的硬件完成，所述的程序可以存储于一种计算机可读存储介质中，上述提到的存储介质可以是只读存储器，磁盘或光盘等。
以上所述仅为本申请的较佳实施例，并不用以限制本发明，凡在本申请的 精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本申请的保护范围之内。

Claims (3)

  1. 一种基于逆向卡尔曼滤波器的Buck变换器故障检测方法，其特征在于，所述方法包括：
    建立非理想Buck变换器在电感电流持续导通情况下的混杂系统离散模型；
    根据所述混杂系统离散模型，获取Buck变换器的状态方程和观测方程；
    获取Buck变换器在工作状态下的输入电压、切换状态、电感电流和输出电压，并确定所述Buck变换器的状态矩阵；
    根据所述状态矩阵、所述状态方程和所述观测方程，按如下公式估计k时刻Buck变换器的参数矩阵，所述参数矩阵中的元素根据Buck变换器中元件的值确定；
    Figure PCTCN2019094386-appb-100001
    Figure PCTCN2019094386-appb-100002
    K(k)＝P(k|k-1)H T(k)·[H(k)P(k|k-1)H T(k)+R] -1；
    Figure PCTCN2019094386-appb-100003
    P(k|k-1)＝P(k-1|k-1)/λ+ΓQ k-1Γ T；
    P(k|k)＝[I-K(k)H(k)]P(k|k-1)；
    根据估计得到的k时刻Buck变换器的参数矩阵，确定Buck变换器中各个元件的估计值；
    根据所述Buck变换器中各个元件的估计值判断所述Buck变换器是否发生故障；
    其中，所述状态方程为X(k+1)＝X(k)+W(k)，所述观测方程为Y(k)＝H(k)X(k)+V(k)；
    X(k)表示k时刻Buck变换器的参数矩阵，Y(k)表示k时刻Buck变换器的观测矩阵，H(k)表示k时刻Buck变换器的状态矩阵，V(k)表示k时刻Buck变换器的观测噪声序列，W(k)表示k时刻Buck变换器的过程噪声序列，V(k)与W(k)相互独立；
    Figure PCTCN2019094386-appb-100004
    表示k时刻参数矩阵X(k)的最优估计结果，
    Figure PCTCN2019094386-appb-100005
    表示利用
    Figure PCTCN2019094386-appb-100006
    进行估计得到的结果，P(k|k)表示k时刻
    Figure PCTCN2019094386-appb-100007
    对应的协方差矩阵，K(k)表示k时刻的卡尔曼滤波增益矩阵，Γ表示噪声驱动矩阵，I表示单位矩阵；λ表示遗忘因子，λ＝1或0＜λ＜1；k为整数；
    Figure PCTCN2019094386-appb-100008
    i L(k)表示k时刻Buck变换器的电感电流，u O(k)表示k时刻Buck变换器的输出电压；
    H(k)＝[i L(k-1)·I 2 u O(k-1)·I 2 S(k)·I 2]，I 2表示二维单位矩阵，S(k)表示Buck变换器中MOSFET管的切换状态；
    Figure PCTCN2019094386-appb-100009
    T表示采样周期，E表示Buck变换器的输入电压，R表示Buck变换器中电阻的值，L表示Buck变换器中电感的值，Buck变换器中电解电容等效为电容和串联电阻，C表示电容的值，R C表示串联电阻的值。
  2. 根据权利要求1所述的方法，其特征在于，所述根据所述Buck变换器中各个元件的估计值判断所述Buck变换器是否发生故障，包括：
    在预定时间范围内，针对所述Buck变换器中每个元件，检测k时刻的估计值与参考值之差是否在预定范围内；预定时间范围为1至N，N为整数，1≤k≤N；
    若检测到k时刻的估计值与参考值之差在预定范围内，则确定所述元件无故障；
    若检测到k时刻的估计值与参考值之差在预定范围外，则检测k+1时刻至k+j时刻的估计值与参考值之差在预定范围外的数量是否为j；j为整数；
    若检测到k+1时刻至k+j时刻的估计值与参考值之差在预定范围外的数量为j，则确定所述元件发生故障；
    若检测到k+1时刻至k+j时刻的估计值与参考值之差在预定范围外的数量不为j，则确定所述元件无故障。
  3. 根据权利要求1或2所述的方法，其特征在于，所述根据估计得到的k时刻Buck变换器的参数矩阵，确定Buck变换器中各个元件的估计值，包括：
    按如下公式确定k时刻Buck变换器中电感的估计值：
    Figure PCTCN2019094386-appb-100010
    按如下公式确定k时刻Buck变换器中电阻的估计值：
    Figure PCTCN2019094386-appb-100011
    按如下公式确定k时刻Buck变换器中用于等效电解电容的串联电阻和电容的估计值：
    Figure PCTCN2019094386-appb-100012
PCT/CN2019/094386 2018-12-12 2019-07-02 基于逆向卡尔曼滤波器的Buck变换器故障检测方法 Ceased WO2020119092A1 (zh)

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