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Observer‐based open transistor fault diagnosis and fault‐tolerant control of five‐phase permanent magnet motor drive for application in electric vehicles

2014; Institution of Engineering and Technology; Volume: 8; Issue: 1 Linguagem: Inglês

10.1049/iet-pel.2013.0949

1755-4543

Mehdi Salehifar, Ramin Salehi Arashloo, Manuel Moreno‐Eguilaz, Vicent Sala, L. Romeral,

Silicon Carbide Semiconductor Technologies

IET Power ElectronicsVolume 8, Issue 1 p. 76-87 ArticleFree Access Observer-based open transistor fault diagnosis and fault-tolerant control of five-phase permanent magnet motor drive for application in electric vehicles Mehdi Salehifar, Corresponding Author Mehdi Salehifar [email protected] Electronic Engineering Department, UPC, Rambla Sant Nebridi, s/n, 08222 Terrassa, SpainSearch for more papers by this authorRamin Salehi Arashloo, Ramin Salehi Arashloo Electronic Engineering Department, UPC, Rambla Sant Nebridi, s/n, 08222 Terrassa, SpainSearch for more papers by this authorManuel Moreno-Eguilaz, Manuel Moreno-Eguilaz Electronic Engineering Department, UPC, Rambla Sant Nebridi, s/n, 08222 Terrassa, SpainSearch for more papers by this authorVicent Sala, Vicent Sala Electronic Engineering Department, UPC, Rambla Sant Nebridi, s/n, 08222 Terrassa, SpainSearch for more papers by this authorLuis Romeral, Luis Romeral Electronic Engineering Department, UPC, Rambla Sant Nebridi, s/n, 08222 Terrassa, SpainSearch for more papers by this author Mehdi Salehifar, Corresponding Author Mehdi Salehifar [email protected] Electronic Engineering Department, UPC, Rambla Sant Nebridi, s/n, 08222 Terrassa, SpainSearch for more papers by this authorRamin Salehi Arashloo, Ramin Salehi Arashloo Electronic Engineering Department, UPC, Rambla Sant Nebridi, s/n, 08222 Terrassa, SpainSearch for more papers by this authorManuel Moreno-Eguilaz, Manuel Moreno-Eguilaz Electronic Engineering Department, UPC, Rambla Sant Nebridi, s/n, 08222 Terrassa, SpainSearch for more papers by this authorVicent Sala, Vicent Sala Electronic Engineering Department, UPC, Rambla Sant Nebridi, s/n, 08222 Terrassa, SpainSearch for more papers by this authorLuis Romeral, Luis Romeral Electronic Engineering Department, UPC, Rambla Sant Nebridi, s/n, 08222 Terrassa, SpainSearch for more papers by this author First published: 01 January 2015 https://doi.org/10.1049/iet-pel.2013.0949Citations: 74AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract To meet increasing demand for higher reliability in power electronics converters applicable in electric vehicles, fault detection (FD) is an important part of the control algorithm. In this study, a model-based open transistor fault diagnsosis method is presented for a voltage-source inverter (VSI) supplying a five-phase permanent magnet motor drive. To realise this goal, a model-based observer is designed to estimate model parameters. After that, the estimated parameters are used to design a sliding mode observer in order to estimate the phase current in an ideal model. Subsequently, the proposed FD technique measures the similarity between the estimated current and real current using cross-correlation factor. This factor is used for the first time in this study to define a FD index in VSI. The presented FD scheme is simple and fast; also, it is able to detect multiple open switch or open phase faults in contrast to conventional methods. On the other side, in order to track reference current of the motor, the estimated parameters are used to design a proportional resonant controller. The FD technique is used to operate a multiphase fault-tolerant brushless direct current (BLDC) motor drive. Experimental results on a five-phase BLDC motor with in-wheel outer rotor applicable in electrical vehicles are conducted to validate the theory. 1 Introduction Nowadays, power converters are widely used in industrial applications. Along the rising applications, there is an increasing demand for higher reliability provided by the power electronic systems in applications such as transportation, electric and hybrid electric vehicle, space craft and more electric aircraft. Fault-tolerant concept is an economic solution to meet this requirement [1]. To accomplish a fault-tolerant system, three main subjects should be considered at the same time in the final design including fault-tolerant design, control and fault diagnosis. Multiphase fault-tolerant permanent magnet (PM) motor drive is a unique solution to achieve high reliability [2]. In the case of a five-phase motor, it is possible to maintain the operation with two faulty phases. Regarding this solution, it is necessary to supply the motor with a fault-tolerant converter. The fault-tolerant converter should be able to detect and isolate the faulty components. According to a recent survey on reliability of power electronics converters [3], power switches are the most vulnerable components in a power converter among others. A complete review of the faulty modes and detection methods in a power converter was conducted in [4]. Open switch and short circuit faults are the most common faults in a power switch among others. The short circuit fault should be detected and removed quite fast; otherwise it can damage the whole system. Nowadays, hardware-based methods are frequently included in commercial gate driver to protect against this fault. On the other side, a solution to detect and protect the open-switch fault is not available in commercial products. If it is not detected, secondary faults may happen. Owing to growing demand for higher reliability by industry, an extensive research has been conducted on open-switch fault detection (FD) methods, recently. Regarding the presented open-switch FD methods in the literature, these methods can be considered in three different categories including signal-based methods, reference-based methods and model-based methods. The signal-based FD schemes have been extensively studied in the literature. To realise a signal-based FD method, the current or voltage signal of the power converter can be used as an input to the FD block. The detection methods based on the voltage signal need extra hardware to detect the fault; as a result, implementation of these methods is expensive. However, these methods are able to detect the fault very fast. Such schemes have been presented in [5, 6]. The FD methods based on the current signal have also been extensively addressed in the literature. Different schemes using tools such as Park's vector modulus, wavelet transform, dc current method, normalised dc current method, Fourier transform and slope method have been presented to obtain a suitable FD index [4]. Low detection speed, complexity, inability to detect multiple faults and sensitivity to fast load transients are the main drawbacks of FD methods based on the current signal. In this category, proposed methods in [7-9] show the highest performance among others. The second type of the open-switch FD method is based on the reference current. According to this method, real current of the converter is measured and compared to the reference current in the control algorithm. After that, a FD index is defined based on the residue value. This method is cheap, fast and robust to the variations of load parameters. Estima and Cardoso [10] presented a FD method based on the reference current. This method cannot be used in a system with open-loop control. The third type of the open-switch FD method is based on the system model. According to this technique, the input signal to the plant is applied to an equivalent mathematical model of the plant, and its response is predicted. In the next step, difference between real output and the predicted signal is used to define the FD index [11-15]. This method is cheap, since extra hardware is not necessary for FD. A FD method based on observer has been presented in [14] to detect multiple open-switch faults in a three-phase induction motor. A bank of observers has been proposed to detect the fault. Consequently, implementation of this method will be even more complicated in the case of a multiphase converter. Shao et al. [16] presented an open-switch FD method based on sliding mode observer (SMO) for application in a modular multilevel converter. To detect the fault, the residue value (i.e. the difference between estimated and real signal) is compared with a fixed threshold value. This approach can lead to false alarm, since the FD index is not independent from load operational conditions. Regarding the model-based FD methods, and to overcome the limitations discussed above, a model-based FD method is presented in this paper. Based on this method, in the first step, the phase currents are estimated by a full state SMO in a fault-tolerant five-phase brushless direct current (BLDC) motor drive. Comparing to conventional model-based methods, which use the residue value (i.e. the difference between measured and estimated state) to define FD index, here cross-correlation technique is proposed to define this index. Inputs to the cross-correlation technique are the measured and estimated current of the power converter. Proposed method still has the advantages of the conventional methods. At the same time, it can effectively detect multiple open-switch or open-phase faults. Furthermore, it is quite robust to transients and parameter uncertainties. An estimator is also designed to estimate the motor parameters. The estimated parameters are used for two purposes. These two purposes are the SMO design and the proportional resonant (PR) controller design. The major contribution of this paper is developing a model-based open transistor FD method. To present the FD technique, the remainder of this paper is organised as follows. The model of the five-phase BLDC motor is explained in Section 2. The current estimation using SMO is presented in Section 3. Proposed FD scheme is presented in Section 4. The FD method is included in a fault-tolerant control algorithm; theory is presented in Section 5. Proposed FD method is used to detect different faulty modes in a five-phase VSI supplying a BLDC motor; experimental results are shown for both FD and fault-tolerant control in Section 6. And finally, the conclusions and remarkable points are presented in Section 7. 2 Model of five-phase BLDC motor The proposed FD technique in this paper intends to implement fault diagnosis in a five-phase VSI supplying a BLDC motor drive, as shown in Fig. 1. Field oriented control (FOC) is used to control the motor; inputs to the control algorithm consist of the phase currents and rotor mechanical position. The same inputs are sent to the FD block. After FD, this block decides the operation mode (i.e. healthy or faulty) of the motor. To isolate the fault, it is necessary to remove the gate signal of the switch in the faulty leg. Fig. 1Open in figure viewerPowerPoint Fault-tolerant BLDC motor drive To implement FD method, in the first step, motor phase currents are estimated based on well-known models. The model in ABCDE reference frame is used because of its less computational requirements and simpler modelling specially under faulty mode. The model of the five-phase BLDC motor with trapezoidal back electromotive force (EMF) under healthy and faulty modes is (1)where i is the phase current, v is the terminal voltage of each phase, R is the equivalent phase resistance, L is the equivalent phase inductance, M1 is the mutual inductance between two adjacent phases, M2 is the mutual inductance between two nonadjacent phases, e is the back EMF in each phase of the motor and vx is the neutral voltage of the motor. The back EMF will be estimated as follows (2)where λm1 and λm3 are the first and third harmonic amplitudes of the rotor flux linkage; ωe is the electrical rotational velocity and ϑ is the rotor electrical angle. To simplify the model under healthy and faulty modes, the model in (1) is redefined in terms of voltage difference between machine terminals as follows (3)From design point of view, in order to increase the reliability of a multiphase fault-tolerant machine, the mutual inductances should be minimised [17]. Due to this fact, and because of small effect of mutual inductances given in (1) and (3), this parameter in the model is neglected in the rest of this paper. It should be noted that under faulty mode, the corresponding row and column of the faulty phase are eliminated from (1). After that, the motor model can be simply redefined in terms of voltage difference between machine terminals similar to (3). The model presented in (3) is utilised to estimate the phase currents and model parameters. The signal estimation methods based on the load model are sensitive to parameter uncertainties and non-modelled dynamics [14]. Consequently, to estimate the phase currents accurately, a full state SMO is applied to the open-loop model. Owing to the observer, the error between real and estimated state variable converges to zero under healthy mode. Details of the designed observer are explained in the next section. 3 Accurate current estimation using SMO As discussed above, the motor phase currents are estimated based on the motor model. The current estimation is realised using two separate observers. An observer is used to estimate model parameters in (3). Other observer (i.e. SMO) is used to estimate motor phase currents; the estimated motor parameters are used in the SMO. Therefore, the motor model used in the SMO is an ideal model. If the motor parameters are known accurately, then estimated currents using the open-loop model will be equal to the real current. However, these parameters are not easily accessible. On the other hand, parameter values can change with temperature and operational condition of the motor. Furthermore, for condition monitoring and control purposes, it is desirable to calculate machine parameters online. To diagnose the fault and design the PR controllers, the motor parameters are estimated in this paper. Estimation method is explained in the next section. 3.1 Stator's parameter estimation In a BLDC motor, the stator parameters (i.e. phase resistance and inductance) have a high effect on the accuracy of the open-loop model. An estimator is designed to calculate the parameters. The basic equations of the machine model given in (1) can be rewritten as (4)where A = R/L and B = 1/L. The goal is to estimate A and B. To improve the estimation accuracy of the open-loop model, a non-linear model reference adaptive observer is designed to estimate the parameters. Estimated currents are as (5)where ^ is used to denote the estimated components. 3.2 Stability analysis To ensure the stability of the estimation algorithm and to design the observers, a stability analysis is done. Here Lyapunov function is used to ensure stability of the system and measurement of parameters. This function is defined as (6)where S is an error function. There are different possibilities to choose the error function [18]. The error function used in this paper is as follows (7)where δ is equal to difference between the estimated and real current in each phase of the power converter and λ is a positive constant. If the error is equal to zero (i.e. S = 0), then, the observer is no longer sensitive to parameter uncertainties. Taking into account (1) and (7), the derivative of S for the first element is calculated as (8) (9)where is equivalent to dx/dt. Similarly, other components are calculated. According to Lyapunov stability theory, if derivative of V is less than zero for all positive V values, then the system is stable [19]. The derivative of (6) is as (10)From (9) and (10), the derivative of V function can be computed as (11)The first element in (11) is negative for λ values less than A. According to Lyapunov stability condition, the remaining components can be calculated as (12) (13)Under steady-state condition, the error and its dynamic are zero. Hence, the resistance and inductance can be calculated from (12) and (13) as follows (14) (15)From (14) and (15), instantaneous values of R and L can be calculated. In this paper, the estimated parameters are used to design the PR controller and to estimate the phase currents using a SMO. As aforementioned, the estimated parameters can be used for other purposes such as improving the controller of the motor. For example, in the case of using a predictive controller in a BLDC motor, it is possible to have both good transient and steady-state performance; however, the controller performance is sensitive to parameter uncertainties. Therefore the parameter estimation can be used to design a robust predictive controller. Detection of high resistance connection in cables feeding the machine has been presented in [20, 21]. To detect a fault in VSI, the phase currents of the motor are predicted; a SMO is used for this purpose. The estimated parameters in (14) and (15) are used in the SMO. Details of SMO are presented in the following section. 3.3 Current estimation To estimate the phase currents, SMO is used in this paper. It has many advantages, which make it a suitable option for the state variable estimation. Simple implementation, robustness to parameter uncertainty and measurement noise are the most important factors among others [16]. As it was shown above, a model reference adaptive observer was used to estimate motor parameters. Since real parameters are already known from the parameter estimator, response of the open-loop model should be equal to real current. In the case of a healthy motor, error signal reduces to zero after few cycles. In presence of a fault, the model-based estimator can no longer estimate the parameters accurately. Under this condition, the error signal increases remarkably. To detect a fault, the error signal available in SMO is compared with a threshold above zero. If it increases beyond the threshold, a fault alarm is generated. Since the estimated parameters are no longer accurate in a faulty motor, the estimated values are always memorised during one cycle before the fault alarm. After the fault alarm, the controller and model parameters are updated with estimated values for one cycle before the fault. To estimate the phase currents accurately, the SMO is designed as (16)where K is the observer gain, and Sat is a saturation function defined as follows (17)It is possible to use different functions instead of Sat such as ‘Sigmoid’ and ‘Sign’ function. The high-frequency oscillations can be avoided in the estimated variables, if the saturation function in (17) is used. To obtain suitable values of K, a stability analysis is presented in the following section. To evaluate stability of the SMO, Lyapunov function is defined as (18)The Lyapunov function and its derivative given in (9) and (10) are similarly adapted here. Taking into account (1) and (18), the derivative of δ for the first element is calculated as (19)Similarly, other components are calculated. Hence, derivative of V function is as (20)Since Sat function is a linear function, sign of δaSat(δa) will be always positive. Consequently, the only condition to achieve sliding surface is for positive K values. According to (19), by choosing higher values of K, dynamic behaviour of resultant error will be even faster. It should be noted that K value has a significant effect on the performance of the proposed FD method. If a very high value is chosen for K, the observed value will follow the real state too fast. Therefore the residue value will be low. On the other hand, by choosing a small value for K, the estimated current will still follow the current pattern before the fault. In this case, it is easier to detect the fault, since the faulty current is significantly different from the healthy current. A low value of K is an optimal choice in this paper. This assumption results in a robust SMO with slow dynamics. This claim will be later validated with experimental results. 4 Fault diagnostic method To detect the fault, it is possible to define a simple FD index (i.e. the error between the estimated and real current values). Developing this approach for a multiphase machine can lead to false alarms. The main reasons are explained in details in the following. When a fault occurs in one phase of the converter, closed-loop control tries to minimise the error between the reference currents and real currents. As a result, in case that the healthy control method is still applied, output voltage of the control block for a faulty inverter will be changed. On the other hand, in the case of a single-switch fault in one phase, a dc value is added to the remaining healthy phase currents. In the case of multiple open-switch faults, the dc value can be very high. Consequently, because of effect of the control method, and faulty signals, the estimated currents in the remaining healthy phases can be different from the real values. In addition, simplifications in model can result in a small error. If estimated and real current values are different, this error can be interpreted as a false alarm based on the error value. As a result, FD block should be robust to these cases. These effects will be later validated by experimental results. To overcome the drawbacks of a simple FD index based on the error function, an alternative solution is proposed in this paper. Here the estimated and measured current signals are fed to a simple unique algorithm. The presented algorithm can detect both the single switch and open-phase faults in a VSI. According to this algorithm, the similarity level between two input current signals is measured as a function of time; this measuring factor is known as cross correlation [22]. This factor is defined as (21)where x1 and x2 are the estimated and measured current in each phase of the power converter, respectively; μ is the moving average value of the input variables and N is the number of samples. It is worth to note that, N value determines the evaluation period in each sampling point. Choosing a small value for N makes the ρ value sensitive to noise. On the other side, a high N value enlarges the detection time. Moreover, the ρ value will be sensitive to frequency transients in a variable speed drive. It should be noted that the smallest value for N is one sample in one period; the highest value is the number of samples in one period of a fundamental frequency. So, a tradeoff should be done between sensitivity to noise and FD speed. The ρ value varies from −1 to 1. In the case of completely similar waveforms, its value approaches to 1. According to (21), under healthy condition in a motor drive, both the estimated and real currents are similar, so the correlation factor is near 1. However, under faulty mode, these waveforms are quite different at least for half of one fundamental cycle. Under faulty mode, the cross correlation factor reduces to zero. So, the ρ factor is a suitable index to distinguish a healthy condition from a faulty condition. In comparison to the conventional methods, the proposed method is robust to all false alarms because of fast load transients or unbalanced non-sinusoidal waveforms. Consequently, a FD index is defined as (22)The D value is equal to zero under faulty mode, while it is close to 1 under healthy mode. Therefore the D value equal to zero indicates a fault condition. To improve the robustness of the proposed FD method against noise and fast transients, here FD is done with a small time delay denoted by td. If the D value is equal to zero during td, then the open switch or open-phase fault is detected. After FD, it is necessary to locate the faulty component in VSI. The fault scenario in one leg of VSI can be either a single-switch fault or an open-phase fault. Owing to the single-switch fault, average value of the phase current during one fundamental cycle is positive in the case of a lower switch fault or negative in the case of an upper switch fault. In the case of the open-phase fault, the phase current and ρ factor are zero. Therefore fault localisation in the case of the single-switch fault is as (23)Here the estimated current is used to localise the faulty switch. To localise the open-phase fault, average value of the ρ factor is calculated during one period as (24)where M is the number of samples in one period. If the average value is zero, then the fault type is an open-phase fault. For the sake of simplicity, aforementioned fault types are codified. The fault codes are 1, −1 and 2 in the case of upper switch fault, lower switch fault and open-phase fault, respectively. These codes are the same in the rest of this paper. Block diagram of the FD method is shown in Fig. 2. In this figure, ε is a small positive value near to zero. Fig. 2Open in figure viewerPowerPoint FD and localisation method Based on the presented technique, fault localisation in the case of a single-switch fault is done during one sampling time after FD. Nonetheless, a time delay around one fundamental cycle is necessary to localise the open-phase fault. As it can be seen from Fig. 2, once the fault is detected, fault localisation block is enabled. It should be noted that, the FD is done separately in each phase of the power converter. As a result, the presented FD technique can be applied to any two-level multiphase VSI. 5 Fault-tolerant control and analysis of a five-phase BLDC motor Application area in this paper is electric vehicles. High reliability is of paramount importance for this application. Five-phase fault-tolerant BLDC motor can meet this requirement. In this paper, fault diagnosis and fault-tolerant control of a multiphase BLDC motor are studied. Block diagram of the studied setup is shown in Fig. 3a. This motor can be operated with one and two-faulty phases. For clarification, motor operational modes are shown with a code denoted by FC in Fig. 3a. The operational control mode of the machine is determined by the FD block developed in Section 4. Here, control modes of the machine are shown by codes 1, 2, 3 and 4, which correspond to healthy mode, one-faulty phase mode, two-adjacent faulty phase mode and two-non-adjacent faulty phase mode, respectively. In the following part, the principals of the fault-tolerant control are briefly reviewed. Fig. 3Open in figure viewerPowerPoint Fault tolerant FOC algorithm a FD, parameter identification and fault-tolerant FOC b Block diagram of the inner current controller under each operational mode of the motor To control the motor, FOC technique is used. The control algorithm is implemented under healthy and each faulty mode, separately. The basic rules used to calculate the reference currents under different fault conditions were shown in [23]. The calculated reference currents in [23] are shown in Table 1. As it can be seen, both first and third harmonics are included in the reference currents. The reference currents are used in this paper in order to realise the fault-tolerant FOC algorithm. Table 1. Optimised phase currents with isolated neutral Current A B C D E one-faulty phase (FC = 2) I1(PU) 0 0.99 0.99 1 0.98 θ1 – 51 137 232 −41 I3(PU) 0 0.17 0.08 0.09 0.19 θ3 – 23 52 186 −19 two-adjacent faulty phases (FC = 3) I1(PU) 0 0 0.59 0.95 0.67 θ1 – – 82 218 0 I3(PU) 0 0 0.12 0.29 0.16 θ3 – – 44 102 41 two-non-adjacent faulty phases (FC = 4) I1(PU) 0 0.99 0 0.98 0.99 θ1 – 77 – 2 −42 I3(PU) 0 0.16 0 0.19 0.17 θ3 – 15 – 55 −21 As it can be seen from Fig. 3a, to implement FOC algorithm, two controllers are used. An outer controller is used to set the motor reference speed shown by ω*. A proportional–integrator (PI) controller is typically used to realise the speed controller. In addition, an inner controller is used to set the motor reference currents shown by i*. The output of the speed controller shown in Fig. 3a is the reference torque denoted by τ*. One main assumption to calculate the optimised reference current values in [23] was no ripples in the generated torque. Therefore authors here use the conventional PI control to set the reference speed. Inner controller can be done in different ways. A comprehensive study has been done on different current controllers in [24]. PI controller in synchronous reference frame and PR controller in stationary reference frame are two possible control methods to set the reference currents. Regarding the optimised reference currents given in Table 1, under faulty mode, the phase currents are unbalanced and non-sinusoidal. In the case of using a simple PI controller, because of unbalanced non-sinusoidal phase currents, both dc component and oscillatory component appear in reference currents after transferring to synchronous reference frame. To have dc reference currents, PI controller should be designed separately for positive and negative sequence components. This implies high computational cost and complicated controller design. Furthermore, PI controller should be able to track harmonic components as well. It is known in the literature that PI controller has a high performance to track dc components [24, 25]. In the case of sinusoidal components; there will be steady-state error. Therefore, the second disadvantage of PI control is poor tracking performance because of its limited bandwidth. As shown in Fig. 3a, in this paper, PR controller in stationary reference frame is used to implement the inner current controller. According to [24], this controller is able to set both positive and negative sequence comp