Detection of PMSM InterTurn ShortCircuit Based on a
Detection of PMSM Inter-Turn Short-Circuit Based on a Fault. Related Disturbance Observer Vasilios C. Ilioudis e-mail: ilioudis@autom. teithe. gr, ilioudis@auth. gr Department of Industrial Engineering and Management, Faculty of Engineering, International Hellenic University (IHU), Thessaloniki, Greece UKSim 2020, Cambridge, 25 -27 March 2020
The Problem of PMSM Sort-Circuit Fault (Inter-Turn Fault) • • • Ø Ø PMSM is frequently exposed to nonideal or even harmful operating conditions (e. g. torque overload, repeated motor starts/stops, inadequate cooling, etc). These undesirable stresses may lead to risk of serious faults or even failures of operation. PMSM faults can be mainly classified as: mechanical faults, associated with bearing faults and air gap eccentricity, magnetic faults (demagnetization), connected with defective distribution of magnetic flux in stator and air gap space, and electrical faults, mainly due to stator winding isolation faults and drive related faults. Short circuits are the most frequent detected faults. The deterioration of the windings insulation is the main reason of stator circuitry failures. Excessive temperatures, electrical or mechanical stress, manufacturing defects and environmental issues are among the main causes of the windings insulation impairment resulting to faulty or damaged PMSM. Insulation damage might lead to a short circuit between different segments of AC machine. Inter-turn or turn-to-turn fault is the most common circuit fault. UKSim 2020, Cambridge, 25 -27 March 2020
Detection and Diagnosis (or even Prognosis) of PMSM Turn-to-Turn Faults Even though the turn-to-urn fault is typically limited only in a small portion of the phase winding associated, this kind of short circuit affects dramatically the PMSM operation causing impaired damages. Therefore methods for early fault detection and machine diagnosis are very important to prevent serious damage and avoid unsafe operation of PMSM. Addressing of inter-turn short circuit problem is most of importance providing accurate information of PMSM operating conditions. Mainly, the developed fault detection techniques can be classified into two strategies: model-based and model-less methods. • Model-based methods are based on modeling and estimation analysis applied in PMSM. In faulty operations, the knowledge of how a PMSM behaves can be obtained through appropriate modeling of the PMSM taking into account the turn-to-turn fault. • Model-less methods can succeed the PMSM fault detection based on the analysis of measured signals, such as currents, voltages, speed and noise. Among them there are Wavelet Packet Analysis (WPA) and Machine Current Signature Analysis (MCSA) UKSim 2020, Cambridge, 25 -27 March 2020
Contribution In this work, a model-based method is proposed to detect phase short-circuit fault in a PMSM based on the faulty dq model through applying the state observer methodology. Typically, this relatively simple technique has the following Beneficial characteristics: ü Development of a new PMSM Model regarding the inter-turn fault at a specific phase windings. ü Design of a Sliding Mode Observer (SMO) for stator flux in succeeding fault detection. ü Implementation of new Voltage Disturbance Observer based on Sliding Mode methodology able to: indicate, quantify and evaluate the fault extend and the characteristics the short circuit. ü Diagnosis or even Prognosis of fault is feasible by means of the equivalent control. ü Effectiveness of the proposed approach is demonstrated through Simulation. UKSim 2020, Cambridge, 25 -27 March 2020
PMSM Model in abc Stationary Reference Frame (Fault Mode) (1) (2) (3) • • • Ncf – Number of short-circuited turns Nch – Number of healthy turns σ - Fault winding fraction rch – Healthy part resistance of phase c rcf – Faulty part resistance of phase c rf – Sort-circuit resistance of phase c Figure 1. A simplified diagram of the faulty stator winding showing the occurred fault in phase c (upper) and the short-circuit of phase c in more details (lower). UKSim 2020, Cambridge, 25 -27 March 2020
Analysis of PMSM Mathematical Model in abc Frame (Voltage/Flux Equations) • ucf - Voltage drop in faulty part uch - Voltage drop in faulty part uc - Voltage of phase c • • (4) (5) Here • • • uabc - Voltage matrix iabc – Current matrix λabc – Stator Flux matrix Fc – Disturbance matrix θabc – 3 -phase angle matrix UKSim 2020, Cambridge, 25 -27 March 2020
PMSM Model in dq Synchronous Reference Frame under c-phase Fault • PMSM Modified Voltage and Flux/Current Model in dq under inter-turn fault: (6) Here (7) • Ks is the transformation matrix from abc to dq reference frame, • ddqf is the voltage disturbance in presence of inter-turn fault, • Js is the skew symmetric matrix. and UKSim 2020, Cambridge, 25 -27 March 2020
Design of Proposed Estimation Strategy based on Sliding Mode Observer (SMO) • Solving Eq. (6) for dλdq/dt, it will be (8) • Sliding Mode Observer (SMO) Design: a) choice of sliding surfaces (manifold), b) choice of discontinuous control input (9) ØStator flux errors in γδ are chosen as sliding surfaces (10 ) ØThe sgn(. ) functions of the flux errors are chosen as control inputs with positive gains kγλ and kδλ UKSim 2020, Cambridge, 25 -27 March 2020
Stator Flux and Voltage Disturbance Estimation • Supposing that the stator flux observer is defined as (11) • and choosing a Lyapunov function candidate (LFC), defined as follows • kd and kq are the observer gains of stator flux. • kr is the observer gain of the stator resistance. (12) then the observer is stable if the first time derivative of Vλ is (13) UKSim 2020, Cambridge, 25 -27 March 2020
Sliding Mode Existence and Observer Stability Conditions §The observer asymptotic stability is ensured, if the derivative of LFC is negative definite, i. e. d. Vλ/dt<0. Consequently, this is valid, if the following conditions are satisfied: §Relations (14) and (15) imply the sliding mode existence. §Moreover, equation (16) is used to design a simple stator resistance observer. (14) (15) (16) (17) üStator resistance observer UKSim 2020, Cambridge, 25 -27 March 2020
Voltage Disturbance Estimation through Equivalent Control • Assuming that the Stator flux observer in (11) and stator resistance estimator in (17) converge considerably fast, the sliding manifold is reached (sdq=0) after finite time tn. Therefore the state trajectories satisfy the initial system equation with the control inputs replaced by their equivalent ones after setting dsdq/dt=0 in (18), and (19), i. e. (18) (19) ØNote that the terms (. )eq represent the equivalent control inputs. Information for the voltage disturbance could be obtained directly by means of low pass filtering (LPF) the control input signals in SMO. UKSim 2020, Cambridge, 25 -27 March 2020
Synopsis of the Estimation Algorithm in an Operating Block Diagram Estimation of PMSM Voltage Disturbance in a Three Steps Process: 1. – – 2. – – 3. – – Calculation of stator flux in dq synchronous rotating frame Inputs: Measured stator voltages, currents and PMSM parameters Output: Stator flux as functions of voltages and stator resistance (real or estimated) Estimation of stator flux in dq (SMO) Inputs: Stator flux components in dq Output: Equivalent Control Signals as functions of stator flux error Stator Voltage Disturbance Estimation (Equivalent control) Input: dq components of stator flux error Output: Estimated voltage disturbances Figure 2. Block diagram of the applied algorithm in obtaining PMSM voltage disturbancestimation. UKSim 2020, Cambridge, 25 -27 March 2020
Parameters of Permanent Magnet Synchronous Machine (PMSM) TABLE I Parameters of PMSM Symbol Se cosφ Vl-l rs Ld Lq λm J p ωm Quantity Expressed in SI electric power coefficient line to line voltage stator resistance d-axis inductance q-axis inductance rotor flux (equivalently) moment of inertia magnetic pole pairs mechanical angular speed UKSim 2020, Cambridge, 25 -27 March 2020 5. 5 k. VA 0. 8 380 V 2. 5Ω 0. 400 H 0. 210 H 0. 54 Vs 0. 039 kgm 2 1 3000 rpm
Simulation Results • The inverter frequency is 8 k. Hz with 520 Vdc voltage of power supply. • The stator voltages and currents are measured to calculate and estimate the stator flux λdq. • SMO observer is employed to detect interturn fault through estimating the voltage disturbance based on equivalent control signals. Figure 3. Block diagram of the controlled PMSM in dq with inter-turn fault. UKSim 2020, Cambridge, 25 -27 March 2020
Simulation Results PMSM Speed at 300 rpm (5 Hz) with Torque 1 Nm (1/5) Stator flux response in dq at 300 rpm: q q q • • Speed changed stepwise from 0 to 10π rad/s Torque of 1 Nm is applied at t 1=1 s and removed at t 2 =3 s. Fault windings ratio σ is equal to 0. 5 and the sort-circuit current if is 4 A. (Upper) Estimated stator flux response (Lower) Stator flux error response Figure 4. Estimated stator flux in dq reference frame (upper), voltage disturbances in d-axis (middle) and q-axis (lower). The speed was changed from 0 to 10π rad/s stepwise, while an external torque of 1. 0 Nm is applied for 2 s. UKSim 2020, Cambridge, 25 -27 March 2020
Simulation Results PMSM Speed at 300 rpm (5 Hz) with Torque 1 Nm (2/5) Voltage disturbances in dq at 300 rpm: q q q • • Speed changed stepwise from 0 to 10π rad/s Torque of 1 Nm is applied at t 1=1 s and removed at t 2 =3 s. Fault windings ratio σ is equal to 0. 5 and the sort-circuit current if is 4 A. (Upper) Estimated and real d-axis voltage disturbance (Lower) Estimated and real q-axis voltage disturbance Figure 5. Estimated voltage disturbances in d-axis (upper) and q-axis (lower). The speed was changed from 0 to 10π rad/s stepwise, while an external torque of 1. 0 Nm is applied for 2 s UKSim 2020, Cambridge, 25 -27 March 2020
Simulation Results PMSM Speed at 600 rpm (10 Hz) with Torque 1 Nm (3/5) Voltage disturbances in dq at 600 rpm: q q q • • Speed changed stepwise from 0 to 10π rad/s Torque of 1 Nm is applied at t 1=1 s and removed at t 2 =3 s. Fault windings ratio σ is equal to 0. 2 and the sort-circuit current if is 5 A. (Upper) Estimated stator flux response (Lower) Stator flux error response Figure 6. Estimated stator flux in dq reference frame (upper), voltage disturbances in d-axis (middle) and qaxis (lower). The speed was changed from 0 to 20π rad/s stepwise, while an external torque of 1. 0 Nm is applied for 2 s. UKSim 2020, Cambridge, 25 -27 March 2020
Simulation Results PMSM Speed at 600 rpm (10 Hz) with Torque 1 Nm (4/5) Voltage disturbances in dq at 600 rpm: q q q • • Speed changed stepwise from 0 to 10π rad/s Torque of 1 Nm is applied at t 1=1 s and removed at t 2 =3 s. Fault windings ratio σ is equal to 0. 2 and the sort-circuit current if is 5 A. (Upper) Estimated and real d-axis voltage disturbance (Lower) Estimated and real q-axis voltage disturbance Figure 7. Estimated voltage disturbances in d-axis (upper) and q-axis (lower). The speed was changed from 0 to 10π rad/s stepwise, while an external torque of 1. 0 Nm is applied for 2 s UKSim 2020, Cambridge, 25 -27 March 2020
Simulation Results PMSM Speed at 600 rpm (10 Hz) with Torque 1 Nm (5/5) Electrical torque response at 300 rpm: q q q Figure 8. Electrical torque response. The speed was changed from 0 to 10π rad/s stepwise, while an external torque of 1. 0 Nm is applied for 2 s Speed changed stepwise from 0 to 10π rad/s Torque of 1 Nm is applied at t 1=1 s and removed at t 2 =3 s. Fault windings ratio σ is equal to 0. 5 and the sort-circuit current if is 4 A. Note that for speed changed stepwise from 0 to 10π rad/s (a) and from 0 to 20π rad/s (b): ü ü ü Stator flux error is about 0. 02 Vs with a maximum of 0. 025 Vs during transition states. Voltage disturbances fluctuate between -2. 25 V to 2. 25 V (s) and – 0. 4 V to 0. 4 V (b). Observer response could be further improved decreasing chattering phenomenon in SMO. UKSim 2020, Cambridge, 25 -27 March 2020
Conclusion • A novel method is developed and tested for detection of PMSM inter -turn fault occurring in a phase. • The proposed scheme was evaluated as an effective estimation approach of the voltage disturbance. This method is based on the dq machine model under fault. It is verified that the applied estimation scheme can efficiently diagnose the effect of short-circuit fault. • In addition, the developed sliding mode observer (SMO) allows very fast convergence and high accuracy on both stator flux and voltage disturbance estimation. • Moreover, simulation results demonstrate that the proposed method is capable to diagnose inter-turn faults even at the early stage for low short-circuit currents. UKSim 2020, Cambridge, 25 -27 March 2020
Future work • Present work has been verified using Matlab / Simulink. • Moreover it will be also validated by experimental results using a DSP based card and a 2. 5 k. W PMSM. UKSim 2020, Cambridge, 25 -27 March 2020
Thank you very much for your attention Vasilios C. Ilioudis e-mail: ilioudis@autom. teithe. gr, ilioudis@auth. gr Department of Industrial Engineering and Management, Faculty of Engineering, International Hellenic University (IHU), Thessaloniki, Greece UKSim 2020, Cambridge, 25 -27 March 2020
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