Fault Detection of Power Electronic Circuit Using Wavelet Analysis in Modelica

Fault Detection of Power Electronic Circuit using Wavelet Analysis in Modelica

Jianbo Gao*, Yang Ji**, Johann Bals**, Ralph Kennel* *Technische Universität München Arcisstr. 21, 80333 Munich, Germany [email protected], [email protected] ** German Aerospace Center Muenchner Str. 20, 82234 Wessling, Germany [email protected], [email protected]

obtain maximum flight reliability and minimum Abstract maintenance efforts, advanced failure analysis tech- nologies shall be applied to ensure correct and quick In more electric aircrafts (MEA) the electric power network is important for the reliability. To prevent fault detection and isolation. It is well known that an severe faults it is the key issue to identify the faults output voltage regulated DC/DC power converter in the early stage before a complete failure happens. supplying constant power loads could de-stabilize In this paper an early stage fault detection method the network stability due to the degraded perfor- using wavelet multi-resolution analysis (MRA) for a mance of its input filter. The sensitivity study of in- regulated buck DC-DC converter is studied. Specifi- put filter parameters concerning the network stability cally, the electrolyte input capacitor is diagnosed. addressed in [2] reveals that the observation of de- The study was carried out using simulation with graded degree of the capacitor in the input filter can Modelica / Dymola. The fault features that were ex- significantly increase the network reliability. tracted from different levels of wavelet decomposition provided clear information for both fast and 1.2 State of the art slow occurring faults. This method showed significant advantages compared with filter techniques. It is Reviewing the considerable development of fault concluded that wavelet transform is a suitable tool diagnosis techniques and many successful applica- for early stage fault detection of the power electron- tions attached to them in the last time [3] [4] [5], ics in MEA. In addition, the simulation language power systems keep a challenge for fault detection. Modelica provides a convenient possibility for the For overcoming this challenge intelligent methods quick design of fault detection strategy. like artificial neural networks have shown their possibilities in this field [6]. Besides, the analytical Keywords: power electronics; DC-DC converter; model based technology is also obtaining more atten- fault detection; wavelet; Modelica; Dymola tion [7] [8] [9]. Signal-based methods, e.g. Fourier transform and 1 Introduction wavelet transform, also provide other possibilities to perform the fault detection and isolation. With the rash development of the new mathematical tool, 1.1 Motivation wavelet transform [10], a great amount of studies The concept of More Electric Aircraft (MEA) is have been done in different fields for fault detection. attracting increasing interest in the aircraft industry Some attempts have also been made in power elec- not only because of its potential in energy optimiza- tronics for fault detection [11] [12]. The implementation, but also due to its significant advantages con- tion of wavelet transform for the post processing of cerning weight, maintenance requirements, liability Modelica simulation data has been seen, for exam- and passenger comfort [1]. For this, the electrical ple, in a study of vehicle steering, where wavelet power distribution network is playing a more im- transform was carried out in the software Matlab for portant role and facing increasing challenges in the calculating power spectra [13]. prognosis and accurate localization of faulty units in an even more complex power network. In order to

DOI Proceedings of the 9th International Modelica Conference 513 10.3384/ecp12076513 September 3-5, 2012, Munich, Germany Fault Detection of Power Electronic Circuit using Wavelet Analysis in Modelica

1.3 Main contributions are used for the transformation, wavelet transform uses different wavelet functions, which can be se- Modelica was developed as a free, object-oriented lected according to the specific problems from a and equation-based modeling language. It has signif- principally unlimited set. Nevertheless, the wavelet icant benefits such as easy reusability of models and function must fulfill some conditions; namely, it multi-domain modeling capability. In combination must be an orthonormal function. The precise math- with the simulation environment Dymola, a conven- ematical description of orthonormality is easily ient platform is provided to the complete model- found in almost every book about wavelet transform, based design and the integration of MEA systems e.g. [10], and is not repeated here. [14]. In contrast to the excellent performance in Parameter, a, defines the width and height of the modeling and simulation, Modelica only supports wavelet function, ψ. A smaller scale, a, makes ψ nar- limited signal analysis features [15], which are actu- rower; thus the wavelet represents fast changes and ally crucial for the fault analysis and virtual testing the transform focuses on the high frequency compo- activities in the verification and validation phase of nents of the signal. Parameter, b, shifts the wavelet the system development. function along the time axis, so that the transform This work focuses on the fast design of a fault de- represents different locations of the signal. Using tection strategy of on board power supply units in different values of scale, a, and position, b, it is able MEA with wavelet transform using Modelica simu- to observe the signal at different position and in dif- lation. To realize this, a wavelet library for Modelica ferent frequency range with only one transformation. is being developed. Multi-Resolution Analysis Thanks to these special properties, wavelet transform (MRA) of wavelet technology is applied to detect the is especially suitable for analyzing changing pro- failure of electrolyte capacitors in a very early stage. cesses. In addition, the design process using Modelica Two forms of wavelet transform are available. simulation shows high flexibility and efficiency. It is They are continuous wavelet transform (CWT) and possible to identify the most important failure fea- discrete wavelet transform (DWT). In CWT both tures and helps to design a effective fault detection scale and position parameters are continuous real strategy within only a short time. values. CWT expresses the signal changes in continuous details. It is more suitable for visual examina- tion. In this work only DWT is used, which will be 2 Wavelet transform described in more detail in the next section.

2.1 Definition 2.2 Discrete wavelet transform

Wavelet transform could be considered as a fur- In DWT only discrete values of the scale and lo- ther development of Fourier transform, or more pre- cation parameters are used. The values are selected cisely, of short time Fourier transform (STFT) [16]. in a discrete form, namely

Using STFT, people try to localize the signal chang- (2) ing with time by selecting suitable time window. , This transformation, however, is limited in time- where and . The transform re- frequency resolution capability due to the uncertainty sults, i.e. the wavelet coefficients, are therefore also principle. Wavelet transform overcomes this prob- discrete. lem. This transform is defined as [10]: In the numeric calculation of DWT, an extra scaling function, in addition to the wavelet function, is . (1) used to carry out a complete and efficient DWT. The It is described as the wavelet transform of the scaling function represents the low frequency com- square-integrable function, f, using wavelet function, ponents of the signal. It is orthogonal to its own dis- ψ, at dilation (or scale), a, and position (or transla- crete translations and to all wavelet functions. The tion), b. The bar above function, ψ, stands for conju- wavelet and the scaling functions with the discrete gation. For the given a and b, the transform result is scaling and translation parameters build a complete a single real number, a wavelet coefficient. orthogonal basis of the Hilbert space. The DWT is Obviously wavelet transform is the integral of the thus another representation of the time signal. multiplication of the signal, f, with a wavelet func- As an example, Figure 1 shows the form of the tion, ψ. It has the same form as the STFT. However, third order Daubechies scaling and wavelet functions not like STFT, where only sine and cosine functions and their Fourier transforms [17].

514 Proceedings of the 9th International Modelica Conference DOI September 3-5, 2012, Munich Germany 10.3384/ecp12076513 Session 4D: Electromagnetic Systems II

2 1 different frequency ranges is obtained, as shown in Scaling function Scaling Figure 3: 1 function Wavelet function h ↓2 cA (k) 0 d0 3 . . . hd0 ↓2 cA2(k) -1 Wavelet function 0 h ↓2 cA (k) h ↓2 cD (k) 0 1 2 3 4 t 0 1 2 3 4 f d0 1 d1 3 (a) (b) f(k) hd1 ↓2 cD2(k) Figure 1: The third order Daubechies scaling and wavelet func- h ↓2 cD (k) tions (a) and their Fourier transforms (b) d1 1

Figure 3: Multi-resolution analysis using DWT

From the Fourier transforms it can be seen that This is the wavelet multi-resolution analysis the scaling function covers lower frequency range (MRA). The output of this operation, cD , cD , …, while the wavelet function stretches in a higher fre- 1 2 cD and cA , are different levels of DWT coeffi- quency range. From this point of view, DWT is actu- n n cients, representing the signal components from ally the division of the time signal into different fre- higher to lower frequencies. Here the original signal quency bands. Thus, it is straightforward to under- is treated as the lowest level of approximation coef- stand that the calculation of DWT is realized using ficients. This analysis provides a convenient tool to filter banks. In inverse DWT the calculation is simi- observe different frequency components of the signal lar. This process is illustrated in Figure 2. depending on time.

hd0 ↓2 cA(k) cA(k) ↑2 hr0 2.4 Wavelet analysis for fault detection f(k) f(k) + Wavelet transform is a powerful tool in signal hd1 ↓2 cD(k) cD(k) ↑2 hr1 processing for the detection of changing events. This DWT Inverse DWT feature is suitable for fault detection since a fault in a system can be treated as a deviation compared to the Figure 2: DWT and inverse DWT calculation using filter banks normal state.

When a fault occurs, specific changes will appear DWT transforms the original sequence in two in the sensor signal. Usually, it is known that the new series: fault signal is located in a certain frequency range, (1) the approximation coefficients, cA(k), represent- but the exact frequency is often unknown or not con- ing the low frequency components, obtained us- stant. This problem can be handled with wavelet ing the low pass filter for decomposition, hd0, MRA. For that, the signal containing fault infor- and mation is firstly decomposed in several levels. And (2) the detail coefficients, cD(k), representing the in one or more levels, where the fault signal frequen- high frequency components, obtained using the cy is located, faults features will be observed. high pass filter for decomposition, hd1. The symbol ↓2 means down sampling. The operation is to delete one from every two adjacent coeffi- 3 Wavelet fault detection in a MEA cients, in order to remove the redundant information. power network system The inverse DWT carries out the reversed operation. The operator, ↑2, expands a coefficient series by in- Based on the properties of wavelet transform in serting a zero between every two adjacent elements. signal processing, this new mathematic tool is used After that the two series pass through the filter bank, for fault detection in a MEA power network system and added together to get the original signal. in this study. Specifically, the MRA is used here to detect the capacitance drop of the input capacitor in a 2.3 Multi-resolution analysis DC-DC buck converter for the early stage failure. Considering the DWT process shown in Figure 2, 3.1 The problem sequence, cA(k), which represents the low frequency components can be further divided into a lower fre- The buck converter is described with the diagram quency part and a higher frequency part inside the shown in Figure 4. frequency range of cA(k). This process is repeated and a series of coefficient sequences representing

DOI Proceedings of the 9th International Modelica Conference 515 10.3384/ecp12076513 September 3-5, 2012, Munich, Germany Fault Detection of Power Electronic Circuit using Wavelet Analysis in Modelica

PWM Switching Uout Feedback pacitance might also occur. For fault detection, espe- Controller cially for early stage fault diagnosis, both stepping Lin Lout Iin Iout type and slow changing of capacitor fault should be Transistor

Cout a considered.

Uin Cin D o Uout

R 3.2 Extraction of fault information Figure 4: Diagram of the Buck converter under study The first step is the extraction of the fault infor- The converter operates in constant load power mation from the sensor signals. Supposing the meas- mode by keeping a constant output voltage, which is ured signal is adjusted through the duty cycle of the pulse width , (3) modulation (PWM) switching signal, which operates where x(k) is the signal in normal operation state, with a constant frequency. Based on the converter and g(k) the additional signal in fault condition. property the system is sensible to the value changes Using wavelet technology, the sensor signal f(k) of the components on the input side, where the input is decomposed with MRA using wavelet function, ψ, capacitor, Cin, is especially critical because it is usu- to obtain wavelet coefficients in n levels: ally an electrolyte type, which has significantly low- , er feasibility and shorter lift time compared with oth- (4) er components. Base on this reason, the early fault , detection is focused on Cin. where Di{.} represents the detail coefficients, and Four parameters of the circuit can be convenient- Ai{.} stands for approximation coefficients. The term ly measured by voltage and current sensors. They Di{.} with smaller index, i, represents higher fre- are, referring to Figure 4, Uout, Iout, Iin and Uin, quency components, namely faster changing signals. ordered from higher to lower ease of availability. The signal, x, in the normal operation condition is Since the load is pure resistive constant load, the composed of the average value of the battery current, output current signal will contain the same infor- which changes very slow, and the ripples caused by mation as the output voltage. And Uout will be used the PWM controlling, which have a constant fre- any way for the controller as feedback, the equip- quency defined by the controller. The slower com- ment of a sensor for output current is therefore not ponents are transformed to the approximation coeffi- necessary, at the least for fault detection. cients, An{x}; and the components with PWM fre- Since a stable output voltage is the control objec- quency, which are higher frequency components, is tive of the circuit, the influence of Cin would be transformed to the very low level of Di{x}. compensated by the controller very quickly. As a On the other hand, the fault signal, i.e. the infor- consequence only very few fault information would mation of the reduction of Cin, is reflected by the be propagated to the output side. The fault detection fluctuation of the input current. As it is known that using Uout is therefore not feasible. the fluctuation frequency is actually the PWM fre- The input voltage is not a good signal for fault quency, most of the fault information is contained in detection, too, since it actually measures the input the PWM components, which means the lower levels power supply voltage, which is normally a voltage of detail coefficients, Di{g}. Depending on the fault source with very low impedance and thus hardly be occurrence rate, complex fluctuation could take influenced by Cin. place. This information will be carried by the PWM The input current is the last possibility; and it is frequency, too, but its own frequency components actually also a suitable signal for fault detection. The are visible in other levels of Di{g}. reason is, for example, if its capacitance drops, it In any circumstance few information will be pre- means the energy capacity of the input circuit is re- sent in very low frequency range, i.e. in An{g}. duced. In order to keep a constant energy flow to the Therefore, we can extract the fault information from load, which is regulated by the controller, Cin would the input current signal simply by isolating some have to be charged and discharged more deeply. This levels of detail coefficients, Di{f}. Of course, the will be reflected in the input current with larger fluc- PWM information will also be involved. It has to be tuation. This estimation will be showed later in the removed before the faults can be identified. Since result section. this frequency is known and it always has a very If an electrolyte capacitor approaches it life end, high value, these components can be easily sup- its capacity would reduce slowly within a certain pressed with low pass filter or band stop filter. time. However, sharp reduction or changing of ca-

516 Proceedings of the 9th International Modelica Conference DOI September 3-5, 2012, Munich Germany 10.3384/ecp12076513 Session 4D: Electromagnetic Systems II

3.3 Fault identification source as 50 kHz. The component fault is simulated by reducing the value of the input capacitor, Cin, After all irrelevant information is excluded the fi- with a ramp source. By setting the ramp, different nal fault information is represented with a single val- changing rate of the component value can be simu- ue, changing according to the failure rate. The fault lated. The input current is measured by a current sen- can be simply identified by comparing it with a sor, which is explicitly put in the model only for known threshold. clarity, since the current values could actually be read out directly from the corresponding components, e.g. Rin or Lin. Other parameters are listed in 4 Design of a fault detection strategy Table 1 using Modelica Table 1: Parameters of the buck converter Because of the aforementioned superior proper- Parameter Description Value ties, Modelica simulation and wavelet transform E Voltage source 54 V were selected for the quick design of a fault detec- Uref Reference output voltage 4.3 V Lout Output inductance 29 μH tion strategy for the power system in MEA. Since Cout Output capacitance 40 μF wavelet transform is not available in the standard Rload Load resistance 1.568 Ω Modelica libraries, a solution have to be found. A Lin Input filter inductance 10 μH seemingly direct solution would be the use of a se- Cin Input filter capacitance 10 μF cond software tool, which provides wavelet analysis Rin Input resistance 0.025 Ω capacity, such as Matlab from MathWorks. Some Kp Propotional controller gain 0.06 Ki Integral controller gain 4.9 practical reasons were faced, however. Firstly, the use of such commercial software requires expensive 4.2 Wavelet transform in Modelica licenses. Secondly, a single program both for simulation and data analysis is very desirable during the The structure of the wavelet toolbox developed work in order to have an integrated working process for Modelica is shown in Figure 6. At the moment of and to avoid interfacing between two programs. It is this report the wavelet library is under development therefore more favourable to have the wavelet analy- within the frame of Clean-Sky project organized by sis inside Modelica. In addition, this brings further European Union. It is expected to be a general advantages in that the library can be a common tool Modelica library with wavelet transform and some of Modelica, so that higher work efficiency will be related functionality for different signal processing achieved in a long term. purposes. This library is used for post processing of the simulation result data and cannot be embedded 4.1 Model of the power supply into simulation models. So far the core library functions have been realized and wavelet DWT and The buck converter shown in Figure 4 is realized MRA can be implemented for the reported work. with a Dymola model in Figure 5.

k=0.06 User‘s Guide k=4.3 +1 fb Transformations Kp + 1-D Continuous Wavelets onOffController k=4.9 - Examples +1 (Functions, Blocks, …) trapezoid refe… add I Uref (MSA, de-noising, …)

u 1-D Discrete Wavelets Ki Applications (Functions, Blocks, …) period=2e-5 Iin Lin Lout Multi-Resolution Analysis 2-D Discrete Wavelets A T 5 L=10e-6 L=29e-6 (Functions, Blocks, GUI, …) (Functions, Blocks, …)

= ramp

R R

C Wavelet Packets

= = U

C Display Wavelets

4 1

o o

0 .

i (1-D, 2-D; Functions, Blocks, …)

u u

a 5

E n

t t

6 U

0 duration=0.1 Basics k=54 Wavelet Families General Functions Interfaces (Functions) ground Figure 5: The Dymola model of the Buck converter for MEA

Figure 6: Structure of the intended Modelica wavelet library (the The voltage controller is a proportional-integral functions with dark background will be designed depending on regulator. The output voltage is set as 4.3 V. The the work process) PWM frequency is defined with the trapezoidal

DOI Proceedings of the 9th International Modelica Conference 517 10.3384/ecp12076513 September 3-5, 2012, Munich, Germany Fault Detection of Power Electronic Circuit using Wavelet Analysis in Modelica

4.3 Process for simulation and fault detection 4.4 Results

As mentioned in the problem description (section The tests with different parameters were carried 3.1) the input current signal is used for fault detec- out. Figure 8 and Figure 9 give two examples with tion. At first the model will be simulated with differ- slow and fast changing faults, respectively. Since all ent reduction rates of the Cin capacitance. The re- fault features mainly present in the first three levels duction rates were selected between 1 and 100 ms of the wavelet decomposition, only these coefficients with a capacitance drop from 10 to 8 μF, correspond- are shown in the figures. ing to 20% capacitance loss. With this fault level the It was noticed that the fault features differed sig- system can still operate normally. However, a 20% nificantly between fast and slow changing rates. For reduction indicates a high possibility of a complete the changing rates faster than 5 ms, a pulse feature failure of the capacitor in the near future. The reduc- appeared in almost every level of the wavelet detail tion is applied at 0.1 s after the startup of the simula- coefficients. This is well seen in Figure 8, where tion so that the system can achieve a stable state be- 20% capacitance drop took place within 1 ms. In the fore the faults could occur. first MRA level the feature magnitude changed from After simulation, the data segment containing the 55 to 70 mA with the fault. In the other two higher fault event will be read out from the simulation result levels the fault event was extra present with pulses. data file. It is converted to equidistant time series The magnitude of the pulses increased with the with a sampling rate of 200 kHz. Equidistant sam- changing rate. The pulses appeared in other higher pling is the requirement of wavelet transform and decomposition level, too. However, in level three it most other signal processing methods. The fault de- was significantly higher than those in other levels. tection process is illustrated in Figure 7. For the fault with 1 ms dropping time, as shown in Figure 8, the pulse peak reached almost 100 mA in Simulation level 3. The simulation showed that for the dropping Sensor data + White noise time up to 5 ms, the peak height reduced linearly to A about 20 mA. Wavelet MRA n (Ignored) For the changing rates slower than 5 ms, the fault D D D 1 2 n features were only significant in the lowest level of Absolu…te value … the wavelet MRA coefficients. Figure 9 shows an example, where the 20% capacitance drop took 100 Low pass filter ms time. Now only the first wavelet decomposition … level contained a fault feature: the feature magnitude Fault features changed from about 55 to 70 mA linearly with the Figure 7: Process for simulation and fault detection using wavelet transform reduction of the capacitance. This was the same as the level 1 feature in fast changing faults. For even lower changing rates this linear relationship was al- To simulate the real world, a white noise signal ways present. Not like in the case of fast changing with normal distribution is added on the input current fault, no significant features were observed in other signal. After that, MRA is applied on the data. The decomposition levels. wavelet function used here was the third order Based on the simulation study, the following fault Daubechies function shown in Figure 1. The detail detection strategy can be defined for early stage fault coefficients in the DWT result are extracted and their detection of the input capacitor, Cin: absolute values are calculated since only the magnitude of the DWT coefficients contains fault infor- (1) In wavelet decomposition level one, if the fea- mation. To remove the high frequency PWM com- ture magnitude exceeds 70 mA, a capacitance ponent, second order Butterworth low pass filter is reduction of 20% of Cin is detected. used. The filter cut off frequency is set as 0.5 kHz, much lower than that of the PWM frequency, in or- (2) In wavelet decomposition level three, if the der to suppress a large part of the noise signal, too. pulse value exceeds 20 mA, the event implies a After this step, different fault features can be visually fast drop of the Cin capacitance. The pulse peak identified and suitable fault detection methods can be value could be used to estimate the capacitance established. changing rate.

518 Proceedings of the 9th International Modelica Conference DOI September 3-5, 2012, Munich Germany 10.3384/ecp12076513 15 15 Session 4D: Electromagnetic Systems II 10 10 5 5 150 15 0.08 0.12 0.16 0.20 (a) 0.24 0 (a) 10 10 0.08 0.12 0.16 0.20 0.24

5 5

0 0 0.08 0.12 0.16 0.20 0.24 0.08 0.12 0.16 0.20 0.24

400 400 (b) (b)

200 200

200 400 4000 200 0.08 0.12 0.16 0.20 0.24 200 0.08 0.12 0.16 0.20 0.24 0 200 200 0 200 2000 -200 (c) 0 (c) 0.08 0.12 0.16 0.20 0.24 0.08 0.12 0.16 0.20 0.24 0 -200 0 0 -200 0.08 0.12 0.16 0.20 0.24 0.08 0.12 0.16 0.20 0.24 0.08 0.12 0.16 0.20 0.24 -200 0.08 0.12 0.16 0.20 0.24 -200 -200 0.08 0.12 0.16 0.20 0.24 0.08 0.12 0.16 0.20 0.24 200 200

200 200 0 (d) 0 (d) 200 200 0 0 -200 -200 0.08 0.12 0.16 0.20 0.24 0 0 0.08 0.12 0.16 0.20 0.24 -200 -200 0.08 0.12 0.16 0.20 0.24 0.08 0.12 0.16 0.20 0.24 -200 -200 0.08 0.12 0.16 0.20 0.24 0.08 0.12 0.16 0.20 0.24 200 200 (e) (e) 200 200 0 200 2100 0 -2000 -210000 0 0.08 0.12 0.16 0.20 0.24 50 0.08 0.12 0.16 0.20 0.24 100 -210000 0.08 0.12 0.16 0.20 0.24 -200 50 100 0.08 0.12 0.16 0.20 0.24 -210000 -2000 50 0.08 0.12 0.16 0.20 0.24 0.08 0.12 00..1166 00..2200 (f) 00.2.244 50 (f) 0 50 50 0.08 0.12 0.16 0.20 0.24 0 0 0.08 0.12 0.16 0.20 0.24 0.08 0.12 0.16 0.20 0.24 0 0 100 0.08 0.12 0.16 0.20 0.24 0.08 0.12 0.16 0.20 0.24 100

1050 100 (g) 50 (g) 100 1050 50 0.08 0.12 0.16 0.20 0.24 0 50 0.08 0.12 0.16 0.20 0.24 50 0 0.08 0.12 0.16 0.20 0.24 0.08 0.12 0.16 0.20 0.24 0 0 0.08 0.12 0.16 0.20 0.24 100 0.08 0.12 0.16 0.20 0.24 100 (h) (h) 100 100 50 50 100 50 50 100 0 0.08 0.12 0.16 0.20 0.24 50 0.08 0.12 0.16 0.20 0.24 0 0 Figure50 8:0 .08 Signals in 0.the12 detection0.16 of a capacitance0.20 drop0. 24 fault Figure 9: Signals0.08 in the0. 1detection2 of0 .1a6 capacitance0.20 drop fault0 .24 0 within 1 ms using wavelet transform. (a) Cin capacitance (μF); within 1000 .0ms8 using wavelet0.12 transform.0.16 (a) Cin 0capacitance.20 0(μF);.24 (b)0 input current signal, Iin (mA); (c-e) detail wavelet coeffi- (b) input current signal, Iin (mA); (c-e) detail wavelet coefficients in 0MRA.08 from Level0.12 3 to level0.16 1 (mA); 0(f.20-h) fault features0.24 cients in MRA from Level 3 to level 1 (mA); (f-h) fault features contained in detail wavelet coefficients of level 3 to level 1 contained in detail wavelet coefficients of level 3 to level 1 (mA). (mA).

DOI Proceedings of the 9th International Modelica Conference 519 10.3384/ecp12076513 September 3-5, 2012, Munich, Germany Fault Detection of Power Electronic Circuit using Wavelet Analysis in Modelica

(a) 4.5 Comparison with filter technique waveletmethod,level1

The wavelet fault detection method was com- filtermethod pared with the traditional filter technique, which was processed according to the procedure as shown in waveletmethod,level3 Figure 10.

(b) waveletmethod,level1 Simulation Sensor data filtermethod + White noise A waveletmethod,level3 High pass filter( fc=10 kHnz)

Absolute value (c) Low pass filter( fc=0.5 kHz) waveletmethod,level1

filtermethod Fault features waveletmethod,level3 Figure 10: Process for simulation and fault detection using filter technique Figure 11: Comparison of the fault features between wavelet The process is similar to that using wavelet trans- method and filter method for (a) 1 ms, (b) 10 ms and (c) 100 ms form. The differences are: fault occurrence rate (black solid line --- level 1 wavelet; blue (1) Instead of wavelet decomposition for removing dashed line --- level 3 wavelet; red solid line --- filter method) the low frequency normal operation signal, a second order Butterworth high pass filter was used. Its cut off frequency was optimized at fc = 5 Conclusion and discussion 10 kHz to keep as much as possible fault information in high frequency range. This work described a method for early fault de- (2) The output of the high pass filter is a single one tection of important electric components in power dimensional time vector, not as in the wavelet supply systems for more electric aircraft (MEA) us- decomposition, where multiple vectors are ob- ing wavelet transform. The special properties of tained. wavelet transform suit this method well for changing signal analysis. The simulation study using Modelica under the environment Dymola illustrated its superi- The fault features obtained using both methods or feasibility for the detection of fast changing faults, for different fault occurrence rates are compared in which was significantly better than the traditional Figure 11. It shows significant advantages of the filter technique. For the slow changing faults, the wavelet method over the traditional filter method. wavelet method also gave a significant feature and For the fast changing faults, the faults were ex- provided clearer information than the filter tech- pressed with both linear change of the feature magni- nique. Based on these advantages, the wavelet fault tude and much sharper pulses in the wavelet method. detection method is expected to achieve satisfied In Figure 11a the pulse peak in the wavelet method detection of early faults. reached about 80 mA from the base line, while the In this study, a specific wavelet library for filter method only showed a peak value of about 10 Modelica is being developed, which possesses the mA. basic functionality of wavelet analysis, including For the slow changing faults, shown in Figure 11a wavelet transform and inverse transform, wavelet and b, although no significant peaks were observed decomposition and reconstruction for multi- in the higher decomposition levels using wavelet resolution analysis, and other related functions. The transform, the features in the first level were still work proved the feasibility of the implementation of clearer than that obtained with the filter method. In wavelet analysis in Modelica. the wavelet method, the features showed a difference More work is being done in this topic, including from 55 to 72.5 mA with a relative change of about further development of the Modelica wavelet library 32%, while the filter method gave a difference from and experimental study of the fault detection with a 34 to 42.5 mA with a difference of only about 25%.

520 Proceedings of the 9th International Modelica Conference DOI September 3-5, 2012, Munich Germany 10.3384/ecp12076513 Session 4D: Electromagnetic Systems II real buck inverter. For a real system, detailed optimi- [9] Y. Ji, J. Bals, Application of model detection zation of the fault detection strategy has to be carried techniques to health monitoring for the elec- out, such as trying other wavelet functions, observ- trical network of More Electric Aircraft, In- ing more changing rates, studying the detection with ternational Conference on Electrical Engi- expanded fault ranges, and considering the faults in neering and applications, 2009. more electrical parts. [10] S. Mallat (2009): A wavelet tour of signal processing - the sparse way. Amsterdam: Elsevier. Acknowledgement [11] H. T. Zhang, Q. An, et al. Fault Detection The authors thank the support from the Clean-Sky Wavelet Fractal Method of Circuit of Three- Joint Undertaking through the Grant Agreement No. Phase Bridge Rectifier. International Confer- 296369 (Project MoMoLib) within the Seventh ence on Intelligent System Design and Engi- Framework Programme of the European Union. neering Application (ISDEA), 2010, S. 725– 729. [12] V. Prasannamoorthy, N. Devarajan, et al. References Wavelet and Fuzzy Classifier Based Fault Detection Methodology for Power Electronic [1] C. Schallert, A. Pfeiffer and J. Bals. Genera- Circuits. International Conference on Process tor power optimisation for a more-electric Automation, Control and Computing aircraft by use of a virtual iron bird, 25th (PACC), 2011, S. 1–6. Internaltional Congress of the Aeronautical [13] T. Buente, A. Sahin, and N. Bajcinca, Naim. Sciences, 2006. Inversion of Vehicle Steering Dynamics with [2] M.R. Kuhn, Y. Ji, D. Schröder, Stability Modelica/Dymola. Proceedings of the 4th In- studies of critical DC power system ternational Modelica Conference 2005, S. comonent for More Electric Aircraft using μ 319–328. th sensitivity. Proc. of the 15 Mediterranean [14] J. Bals, Y. Ji, M. R. Kuhn, C. Schallert, Conference on Contro & Automation, 2007. Model based design and integration of More [3] J. Gertler. Fault Detection and Diagnosis in Electric Aircraft systems using Modelica. Engineering Systems. Marcel Dekker, 1998. Moet forum at European power electronics [4] J. Chen and P.Patton. Robust Model-based conference and exhibition, 2009. Fault Diagnosis for Dynamic Systems. [15] Y. Ji, J. Bals, A Modelica signal analysis tool Kluwer Academic Publishers, 1999. towards design of More Electric Aircraft, ICIAE, 2010. [5] S. X. Ding. Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms [16] E. Jacobsen and R. Lyons. The sliding DFT. and Tools. Springer Berlin, 2008. Signal Processing Magazine, vol. 20, issue 2, pp. 74–80, March 2003. [6] K. Swarup and H. Chandrasekharaiah. Fault detection and diagnosis of power systems us- [17] I. Daubechies. Ten Lectures on Wavelets. ing artificial neural networks. 1st internation- SIAM 1992. al forum on application of neural networks to power system, 1991. [7] M. Aldeen and F. Crusca. Observer-based fault detection and identification scheme for power systems: Generation, Transmission and Distribution. lEE Proceedings, vol. 153, pp.71-79, 2006. [8] Y. Ji and J. Bals. Multi-Model Based Fault Detection for the Power System of More Electric Aircraft. Proceedings of the 7th Asian Control Conference, Hong Kong, Chi- na, Aug. 27-29, 2009.

DOI Proceedings of the 9th International Modelica Conference 521 10.3384/ecp12076513 September 3-5, 2012, Munich, Germany Fault Detection of Power Electronic Circuit using Wavelet Analysis in Modelica

522 Proceedings of the 9th International Modelica Conference DOI September 3-5, 2012, Munich Germany 10.3384/ecp12076513