Method for determining stability boundary of motor simulator considering inter-turn short circuit motor model
Patent Information
- Application Number
- CN202611230313.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-13
- Publication Date
- 2026-10-20
Smart Images
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Abstract
Description
Technical Field
[0001] This application belongs to the field of motor simulation and power stage hardware-in-the-loop testing technology, specifically providing a method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model. Background Technology
[0002] Electric motors are core components of new energy vehicles. Because they frequently operate in high-power, complex, and harsh environments, they are prone to various electrical faults. Among these, inter-turn short circuit (ISCF) in the stator winding is one of the most common fault types, accounting for approximately 30% to 40% of all motor faults. After an ISCF occurs, the short-circuit circuit experiences severe localized heating, which can easily lead to insulation failure, increased torque fluctuations, and irreversible demagnetization of permanent magnets, directly threatening the safe operation of the drive system. Therefore, achieving safe, controllable, and repeatable simulation of inter-turn short circuit conditions during the motor development stage has significant engineering value for revealing fault mechanisms, verifying diagnostic algorithms, and developing fault-tolerant strategies.
[0003] The MCU-EME reverse-drive test system is a power hardware-in-the-loop (PHIL) test platform that replaces traditional mechanical bench testing methods. The Electric Motor Emulator (EME) accurately simulates the port electrical characteristics of a real motor by solving the motor model in real time and controlling power switching devices, providing an ideal test environment for verifying the drive strategies of the Motor Control Unit (MCU). Using the MCU-EME reverse-drive test system to test for inter-turn short circuit conditions allows for the safe, controllable, and highly repeatable injection of faults of varying severity, thus providing a repeatable test environment for fault diagnosis algorithms and protection strategies without damaging the real motor.
[0004] However, when simulating inter-turn short-circuit faults using a motor model, the electrical parameters of the motor stator windings change, introducing an additional short-circuit loop. This transforms the motor model in the dq-axis coordinate system from a linear time-invariant (LTI) system into a periodic time-varying system. Once this model is embedded into the control loop of the MCU-EME-based drag test system, the original LTI system state equations will transform into periodic time-varying state-space equations. Most existing stability analysis methods are based on the assumption of linear time-invariant systems, making them difficult to directly apply to such periodic time-varying systems. Consequently, they cannot accurately assess the stable operating boundary of the drag test system under inter-turn short-circuit conditions. This leads to the simulator being misused for fault reproduction testing even when it exceeds the actual stable operating speed range, resulting in distorted test results and potentially causing equipment protection tripping or damage. Summary of the Invention
[0005] This application provides a method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model through embodiments, including the following steps: An inter-turn short-circuit motor model is established, which includes inter-turn short-circuit parameters used to characterize the severity of inter-turn short circuits, and the transfer matrix of the inter-turn short-circuit motor model is a periodic time-varying matrix related to the inter-turn short-circuit parameters and the electrical angle of the motor. Establish a control model for the MCU-EME-to-drive test system that takes into account time delay. The EME-side control model adopts a current tracking strategy based on feedforward compensation and state feedback. The feedforward compensation voltage and the state feedback voltage are determined based on the inter-turn short-circuit motor model and the coupling inductance of the MCU-EME-to-drive test system. The MCU-EME control model and the EME control model are combined to establish a periodic time-varying state model of the MCU-EME drag test system for inter-turn short circuit conditions. The stability of the periodic time-varying state model is analyzed to determine the stability boundary of the motor simulator considering the inter-turn short-circuit motor model.
[0006] The method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model provided in this application introduces short-circuit parameters reflecting the severity of the inter-turn short circuit into the motor model, enabling the motor model to accurately characterize the changes in the motor's electrical characteristics after an inter-turn short-circuit fault occurs. Furthermore, the inter-turn short-circuit motor model is combined with the MCU-side control model and the EME-side control model to establish a state model that accurately describes the time-varying characteristics of the test system. Stability analysis is then performed on the time-varying system state model to clarify the safe operating boundary of the motor simulator under inter-turn short-circuit conditions. This effectively solves the problem that existing stability analysis methods, based on the assumption of linear time-invariant systems, fail when faced with inter-turn short-circuit conditions. Attached Figure Description
[0007] Figure 1 This is a schematic diagram of the architecture of the MCU-EME drag test system; Figure 2 This is a flowchart of a method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model, according to an embodiment of this application. Figure 3 This is a schematic diagram of the stator winding topology of a permanent magnet synchronous motor used to simulate inter-turn short-circuit conditions. Figure 4 This is a schematic diagram of the MCU-EME-to-tow test system for inter-turn short-circuit conditions provided in the embodiments of this application; Figure 5 This is a schematic diagram of the EME-side control strategy in the MCU-EME-tow test system for inter-turn short-circuit conditions provided in the embodiments of this application; Figure 6 This is a graph showing the variation of eigenvalues of the state transition matrix of the drag test system under different short-circuit coefficients according to embodiments of this application. Figure 7 This is a simulation diagram of an MCU-EME-to-tow test system for inter-turn short-circuit conditions provided in an embodiment of this application. Figure 8 This is a schematic diagram illustrating the speed-up simulation results of the MCU-EME-based drag test system under different short-circuit coefficients according to the embodiments of this application. Figure 9 This is a physical diagram of the MCU-EME towing test system for inter-turn short-circuit conditions provided in the embodiments of this application; Figure 10 This is a schematic diagram illustrating the speed-up test results of the MCU-EME for the towing test system under different short-circuit coefficients according to the embodiments of this application; Figure 11 This is a comparison chart of the stability analysis results of a motor simulator considering an inter-turn short-circuit motor model provided in the embodiments of this application. Detailed Implementation
[0008] The present application will now be further described based on preferred embodiments and with reference to the accompanying drawings.
[0009] Figure 1 This is a schematic diagram of the architecture of an MCU-EME parallel testing system. This parallel testing system can be used to provide a hardware-in-the-loop test environment for verifying the control strategy of a motor control unit (MCU). It mainly consists of two parts: a motor controller (MCU) and an electric motor emulator (EME). The MCU side and the EME side are interconnected through a coupling inductor to simulate the impedance characteristics of a real motor winding and to filter high-frequency harmonic components.
[0010] Specifically, as shown in the figure, the EME side consists of a motor model, an EME side controller, and an EME side inverter. The three-phase current collected on the right side of the coupling inductor is transformed to the dq axis and compared with the dq axis current calculated by the motor model on the EME side in a current closed loop. The resulting current error is processed by the EME side controller to generate a corresponding PWM control signal, which is used to control the switching action of the EME side power inverter, thereby reproducing the back EMF and current characteristics that the simulated motor should have on the coupling inductor.
[0011] The MCU side consists of an MCU side controller and an MCU side inverter: the three-phase current collected from the left side of the coupling inductor is transformed to the dq axis and then compared with the externally given dq axis reference current in a current closed loop. The resulting current error is processed by the MCU side controller to generate a corresponding PWM control signal, which is used to control the switching action of the MCU side power inverter, thereby outputting the corresponding drive voltage.
[0012] The MCU side and the EME side are connected via a coupling inductor, forming the following signal transmission relationship: the drive voltage output by the MCU-side inverter is transmitted to the EME side via the coupling inductor, serving as the excitation input sensed by the EME-side motor model; simultaneously, the EME-side inverter, based on the motor model calculation results, drives the back EMF and current reproduced by the EME-side power inverter, which are fed back to the current sampling stage on the MCU side via the coupling inductor, forming the feedback quantity for the MCU-side current closed-loop control. Thus, the MCU side and the EME side form a complete closed-loop electrical circuit through the coupling inductor, enabling the MCU-side controller to establish a complete power closed loop with the EME-side "virtual motor," receiving real current and voltage excitation and feedback, thereby achieving hardware-in-the-loop verification of the MCU control strategy.
[0013] When the motor model embedded in the EME is replaced from a healthy motor model to a motor model with an inter-turn short-circuit fault, the voltage and current characteristics reproduced on the coupled inductor become the characteristics exhibited by the motor under the inter-turn short-circuit fault condition. Consequently, the drive feedback signal received by the MCU-side controller also transforms into the current and voltage response under the inter-turn short-circuit condition. This can be used to test the adaptability of the MCU-side drive strategy, the effectiveness of the fault identification algorithm, and the reliability of the corresponding protection and response strategies when the motor has an inter-turn short-circuit fault. In the embodiments of this application, this drag-and-drop test system with a motor model containing an inter-turn short-circuit fault embedded in the EME is called the MCU-EME drag-and-drop test system for inter-turn short-circuit conditions.
[0014] After replacing the motor model with one containing an inter-turn short-circuit fault, the motor simulator faces new technical challenges in accurately reproducing the electrical characteristics of the real motor under inter-turn short-circuit conditions. On the one hand, because the electrical parameters of the motor stator winding change after the inter-turn short circuit occurs and an additional short-circuit loop is introduced, the inductance, resistance and other parameters of the short-circuit winding will change periodically with the electrical angle, causing the motor model in the dq axis coordinate system to change from a linear time-invariant system to a periodic time-varying system, and the system state matrix exhibits periodic time-varying characteristics. On the other hand, the high-order harmonics of the current excited to simulate the inter-turn short-circuit condition will also be coupled with the inherent control delay, discretization and other aspects of the motor simulator system itself, further aggravating the risk of instability of the system in the higher speed range.
[0015] Existing stability analyses for motor simulators can be broadly categorized into four types: The first type is frequency domain analysis based on single-input single-output (SISO), which assesses the impact of delay and bandwidth on system stability through open-loop Bode plots; the second type is a complex vector-based modeling method that incorporates speed-related cross-coupling terms into the transfer function in the complex domain, enabling the analysis of high-speed instability mechanisms within the SISO framework; the third type is a state-space method based on multiple-input multiple-output (MIMO), which determines stability through system eigenvalue distribution or pole trajectories; and the fourth type is a stability analysis method for multi-rate systems, which focuses on examining the interaction effects of multiple time-scale discretized components within the EME, such as the motor model (microsecond level), control algorithm (tens of microseconds level), and power switch (hundreds of microseconds level).
[0016] The core limitation of the above-mentioned stability analysis methods is that they all assume that the controlled object is a linear time-invariant system under the dq system (at a specific speed). They cannot effectively handle the periodic time-varying parameters (such as electrical angle) introduced by the inter-turn short circuit fault, and it is difficult to accurately characterize the stability boundary migration phenomenon caused by the periodic change of the system state matrix with the electrical angle. Therefore, they cannot accurately evaluate the safe operating boundary of the motor simulator in reproducing the inter-turn short circuit fault condition. (It should be noted that the stability boundary determined here refers to the stability boundary of the motor simulator control system itself. That is, after exceeding this boundary, the motor simulator control system will become unstable, resulting in current divergence, protection action and even equipment damage, so that it can no longer accurately reproduce the electrical characteristics under the fault condition. It is not the physical instability phenomenon such as thermal runaway, insulation failure and demagnetization exhibited by the real motor after the inter-turn short circuit. The two are fundamentally different in meaning.)
[0017] Therefore, it is urgent to construct a stability criterion suitable for periodic time-varying systems for motor simulators after inter-turn short-circuit faults are injected, in order to determine the influence of the degree of short-circuit fault on the instability boundary electric speed of the system, thereby providing reliable support for parameter tuning and safe operation boundary determination of the test system under inter-turn short-circuit conditions.
[0018] To achieve the above objectives, this application provides a method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model through embodiments, such as... Figure 2 As shown, the method includes the following steps: Step 100: Establish an inter-turn short-circuit motor model. The inter-turn short-circuit motor model includes inter-turn short-circuit parameters used to characterize the severity of inter-turn short circuits, and the transfer matrix of the inter-turn short-circuit motor model is a periodic time-varying matrix related to the inter-turn short-circuit parameters and the electrical angle of the motor. Step 200: Establish the MCU-side control model and EME-side control model of the MCU-EME-to-drive test system considering the delay. The EME-side control model adopts a current tracking strategy based on feedforward compensation and state feedback. The feedforward compensation voltage and state feedback voltage are determined based on the inter-turn short-circuit motor model and the coupling inductance of the MCU-EME-to-drive test system. Step 300: Combine the MCU-side control model and the EME-side control model to establish a periodic time-varying state model of the MCU-EME-to-tow test system for inter-turn short-circuit conditions. Step 400: Analyze the stability of the periodic time-varying state model to determine the stability boundary of the motor simulator considering the inter-turn short-circuit motor model.
[0019] Through the above steps, a periodic time-varying state model of the towing test system that accurately characterizes the electrical characteristics of inter-turn short-circuit faults can be established. Based on this, the stability of the motor simulator injected with inter-turn short-circuit faults can be analyzed in a targeted manner. This overcomes the technical problem that existing stability analysis methods do not consider the time-varying characteristics of the system caused by inter-turn short-circuit conditions, which leads to the failure of stability analysis methods and the inability to accurately assess the safe operating boundary of the system.
[0020] The following detailed explanation of the specific implementation of each step, in conjunction with the accompanying drawings, provides a detailed description.
[0021] <Step 100> Step 100 is used to establish a mathematical and physical model that can simulate the electrical characteristics of the motor under a short-circuit fault in the stator winding, and use it to replace the healthy motor model in order to introduce the short-circuit condition in the towing test system.
[0022] Taking a permanent magnet synchronous motor (PMSM) as an example, it is understandable that for other types of motors, such as hybrid excitation synchronous motors, the same method can be used to inject inter-turn short-circuit faults into the corresponding healthy motor model.
[0023] Figure 3 This diagram illustrates the stator winding topology of a permanent magnet synchronous motor with an inter-turn short-circuit fault. The short-circuit fault occurs in phase a winding. To represent this fault, a local short-circuit loop can be artificially created inside phase a winding. This short-circuit loop is connected in parallel with the healthy winding segment of phase a winding, together forming a... Figure 2 The diagram shows the stator winding topology of a PMSM under inter-turn short-circuit conditions.
[0024] An inter-turn short-circuit loop forms an additional current path within the phase a winding. When current flows through the phase a winding, a short-circuit current is induced in this loop. The magnitude of the short-circuit current depends on both the equivalent resistance of the short-circuit loop itself and the ratio of the number of turns in the short-circuited winding to the total number of turns in the phase a winding. Therefore, two inter-turn short-circuit parameters can be introduced to characterize the severity of the fault, one of which is the short-circuit resistance. This represents the equivalent resistance of the inter-turn short-circuit loop itself. The smaller the resistance value, the lower the contact resistance at the short-circuit point, and the more severe the short-circuit fault. Another inter-turn short-circuit parameter is the short-circuit coefficient. This represents the proportion of the number of short-circuited winding turns to the total number of winding turns in its phase, and its value ranges from 0 to 1. The larger the value, the higher the proportion of short-circuited winding turns. This is understandable, as... When the value is 0, there are no short-circuited winding turns in the short-circuit loop. Figure 2 The stator windings will degenerate into a healthy motor without inter-turn short-circuit faults.
[0025] use Figure 2 The stator winding topology shown can be used to establish a turn-to-turn short-circuit motor model. Specifically, coordinate transformation is performed on the voltage equations of the three phases abc and the turn-to-turn short-circuit loop to obtain the dq-axis voltage equations under the injected turn-to-turn short-circuit fault: (1), in: (2), The current in the short-circuit loop is expressed as: (3).
[0026] In equations (1) to (3), , These are the d-axis and q-axis voltages (V) output from the MCU side, respectively. , These are the original d-axis and q-axis currents (A) of the stator windings, respectively. , These are the equivalent d-axis and q-axis currents (A) of the stator winding after short-circuit current coupling correction. , These are the d-axis and q-axis inductances (H), respectively. For stator resistance ( ); The electric speed of the motor (rad / s); For permanent magnet flux linkage (Wb); , As mentioned above, these are the inter-turn short-circuit resistances ( and short-circuit factor, The electric angle of the motor.
[0027] Substituting equations (2) and (3) into equation (1) and rearranging them into state-space form: (4), in: .
[0028] Understandable, This represents the original dq-axis current vector of the stator winding. This is the equivalent dq-axis current vector of the stator winding after correction for short-circuit current coupling. This is the coefficient matrix of the inter-turn short-circuit motor model. This is the input matrix for the inter-turn short-circuit motor model. Let be the back electromotive force disturbance vector caused by the permanent magnet flux linkage and the electric speed. In the inter-turn short-circuit motor model The corresponding output matrix is a 2D identity matrix. This refers to the dq-axis voltage vector output from the MCU side. This is the transfer matrix for the inter-turn short-circuit motor model.
[0029] Equation (4) is the state-space equation form of the inter-turn short-circuit motor model.
[0030] Observing equation (4) and the expressions of its matrices, it can be seen that due to the injection of inter-turn short-circuit faults, the transfer matrix... The time-invariant matrix is transformed into the inter-turn short-circuit parameters ( and ) and the electrical angle of the motor The relevant periodic time-varying matrix, specifically, This reflects the coupling relationship between the short-circuit loop and the healthy winding as a function of electrical angle. Periodic changes, the intensity of which is related to and Related, correspondingly The additional distortion current that is generated due to the inter-turn short circuit is periodically changing. This periodic time-varying term causes the motor model described by equation (4) to change from a linear time-invariant system corresponding to a healthy motor model to a periodic time-varying system.
[0031] The motor model for injecting inter-turn short-circuit faults established in step 100 introduces a short-circuit coefficient. With short-circuit resistance These two inter-turn short-circuit parameters enable a quantitative description and continuously adjustable control of the severity of inter-turn short-circuit faults. They also reveal the key physical phenomenon that inter-turn short-circuit faults cause the motor model state matrix to exhibit periodic time-varying characteristics. This provides a core component for establishing a periodic time-varying state model of the towing test system for inter-turn short-circuit conditions in the subsequent step 300.
[0032] <Step 200> Step 200 is used to establish the MCU-side control model and the EME-side control model in the drag test system. In the process of modeling the MCU-side control model and the EME-side control model, the drag architecture based on MCU-EME needs to consider the impact of coupling inductance and delay on the control model.
[0033] a. Coupled inductor modeling The coupling inductor is the physical connection element between the inverter on the MCU side and the EME side. It is used to simulate the motor winding impedance and filter out high-frequency harmonics to form a power closed loop between the MCU and the EME. Generally, the impedance mismatch between the motor winding and the coupling inductor can be solved by adding feedforward compensation to the control strategy on the EME side. Therefore, it is necessary to establish a coupling inductor model as the basis for feedforward compensation on the EME side.
[0034] Specifically, the coupled inductor model in state-space equation form can be established using the following formula: (5), in: , In the formula, The resistance value of the coupling inductor ( ), The inductance value (H) is the value of the coupling inductance. , These are the d-axis and q-axis currents (A) of the coupled inductor, respectively. Let dq be the current vector of the coupled inductor. , These are the d-axis and q-axis voltages (V) output from the EME side, respectively. This refers to the dq-axis voltage vector output from the EME side. This is the coefficient matrix of the coupled inductor model. In the coupled inductor model The corresponding input matrix, In the coupled inductor model The corresponding input matrix.
[0035] b. Delayed expression The MCU-side output voltage serves as the command voltage for the EME side. Meanwhile, the EME-side output voltage needs to be sampled and fed back. Since both the command voltage and the feedback voltage are output through a switching power inverter, there is discretization of the control cycle and the switching execution during the output process, which inevitably leads to a lag in the voltage output execution.
[0036] Specifically, current and rotor position information are typically sampled by the PWM control cycle, with the sampling period equal to the PWM control cycle. This introduces a complete sampling period delay; simultaneously, from the calculation of the voltage reference value to the actual PWM waveform output, due to the digital processing and modulation process, approximately [a delay is typically generated]. The delay, especially at high speeds, will also cause a significant coordinate system angle deviation, resulting in output voltage distortion. Considering all these factors, the overall delay consists of the following two parts: (1) Sampling period delay term: (6), in To control latency, generally, .
[0037] (2) Voltage amplitude and phase distortion terms: (7), in It is the imaginary unit.
[0038] Generally, the amplitude distortion is approximately 1, and the phase distortion can be written in the following matrix form: (8).
[0039] Equations (6) and (8) give the expressions for the overall delay term when establishing the MCU-side control model and the EME-side control mode. By substituting the parameters of the actual power devices into these expressions, the actual values can be determined.
[0040] c. MCU-side control model In some preferred embodiments, the MCU-side control employs an internal model control (IMC) strategy. Figure 4 The MCU-side control block diagram considering delay is shown, such as Figure 4 As shown, the MCU-side controller input is a given dq-axis reference current. The state variables calculated from the motor model for injecting inter-turn short-circuit faults. The output is voltage. A state-space equation form for the MCU-side control model can be established as shown in the following equation: (9), in: .
[0041] in, The state vectors of the MCU-side internal model decoupling controller, including the internal state vectors. ( , (These are its d-axis and q-axis components, respectively) and the output state vector. ( , These are its d-axis and q-axis components, respectively. , These are the d-axis and q-axis command currents on the MCU side, respectively. This is the dq-axis command current vector on the MCU side. The coefficient matrix of the MCU-side control model. In the MCU-side control model The corresponding input matrix, In the MCU-side control model The corresponding input matrix, The output matrix of the MCU-side control model. This is the control delay on the MCU side, typically the MCU side sampling period. 1.5 times, This is the phase distortion matrix caused by the delay on the MCU side.
[0042] Furthermore, , Each is controlled by the internal model control parameter matrix. , , , The structure consists of the control parameter matrices of each internal model. , , The control parameters for decoupling the internal model can be controlled by the MCU bandwidth. Determine the motor parameters: , , .
[0043] d. EME-side control model Figure 5 The diagram illustrates the EME-side control block diagram considering time delay. In some preferred embodiments, the EME-side control model employs a current tracking control strategy based on feedforward compensation and state feedback. Feedforward compensation addresses the impedance parameter mismatch between the motor windings and the coupled inductor; state feedback suppresses the drift of the coupled inductor parameters caused by factors such as temperature rise and magnetic saturation, thereby resolving EME modeling errors. The model input is the voltage vector output from the MCU side. The output is the current vector on the coupled inductor. .
[0044] For the feedforward compensation stage, the motor equations and coupled inductor equations for the injection of inter-turn short-circuit faults are combined: (10) The feedforward compensation voltage is calculated based on the following formula. : (11), in: , In the formula, The nominal value (H) of the coupling inductance; The nominal value of the coupling inductor resistance ( Accordingly, Based on nominal parameters ( , The determined coupling inductance coefficient matrix, Determined based on nominal parameters The corresponding coupled inductor input matrix, Determined based on nominal parameters The corresponding coupled inductor input matrix.
[0045] For state feedback, a linear quadratic optimal control (LQR) approach can be used, and the feedback gain matrix can be obtained by solving the Riccati equation. : (12), in, , It is a weighted matrix and requires Non-negative definite, Positive determination. Through adjustment... and Changeable .
[0046] To adapt to changes in rotational speed, preferably, , The possible values are: , Using matrices with non-zero secondary diagonals The coupling cost between dq-axis currents can be incorporated into the performance specifications to effectively suppress the cross-coupling effect between dq-axis currents, thereby obtaining the feedback compensation voltage. for: (13).
[0047] Adding equations (11) and (13), we can obtain the EME-side voltage before considering the delay: (14).
[0048] because It does not act directly on the coupled inductor, but becomes after propagation delay and voltage phase distortion. Then, acting on the coupled inductor, this process can be represented as: .
[0049] Will Substituting the expression into equation (10), we obtain the EME-side control model in the form of a state-space equation considering time delay: (15) in: , in, This is the internal state vector of the EME-side controller. This is the EME-side control delay, typically the EME-side control cycle. 1.5 times, This is the phase distortion matrix caused by EME-side delay. , This is the autonomous term matrix with delay on the EME side. As shown above, this is the feedback gain matrix. , , The intermediate matrix is determined for a current tracking strategy based on feedforward compensation and state feedback.
[0050] <Step 300> Since the essence of a motor simulator is to... Figure 4 Replace the motor model in the middle with Figure 5In the EME model, during the establishment of the MCU-side control model and the EME-side control model, the coupling inductance factor, the delay factor, and the motor model for injecting inter-turn short-circuit faults have been introduced respectively. Therefore, by combining equations (9) and (15), we can obtain the periodic time-varying state model of the MCU-EME-tug test system for inter-turn short-circuit conditions, characterized in the form of state-space equations: (16).
[0051] As you can see, This is the coefficient matrix of the entire drag test system, used to couple the states of the MCU side and the EME side. In the embodiments of this application, it is defined as the MCU-EME coupling coefficient matrix. This means, that is: , Accordingly, equation (16) can be written as: (16').
[0052] As you can see, It includes a time-varying term that varies periodically with the electrical angle due to the injected inter-turn short-circuit fault (specifically, in the coupling coefficient matrix). This term originates from the periodic time-varying coupling distortion transfer matrix of the motor model itself caused by the injected inter-turn short circuit in step 100. Therefore, the state model of the MCU-EME drag test system described by equation (16) or (16') is a periodic time-varying state model, rather than a traditional linear time-invariant state model.
[0053] <Step 400> Since the coefficient matrix in equation (16) contains time-varying terms, the conventional Lyapunov first method cannot be used to judge stability based on whether the poles are distributed on the left side of the Gaussian plane. It is necessary to introduce a stability criterion for periodic time-varying systems. According to Floquet theory, for a time-varying system: If the coefficient matrix Satisfying periodicity conditions ,in To determine the period of this periodic time-varying system, the matrix differential equation can be solved numerically: (17) from Points to The coefficient matrix is obtained. Single-period state transition matrix , then calculate eigenvalues (i.e., Floquet multipliers), if the following conditions are met: (18) Then the time-varying system is asymptotically stable.
[0054] Meanwhile, according to control theory, if the coefficient matrix of a time-varying system satisfies: (19) The state transition matrix can then be written in the form of an exponential function: (20).
[0055] However, for the state-space equation shown in equation (16), satisfying the condition in equation (18) is equivalent to satisfying: (twenty one).
[0056] Substitution The expression (21) does not hold, therefore It cannot be expressed as an exponential function as shown in (20), therefore, the stability analysis of the MCU-EME cannot be performed by solving the problem after an inter-turn short-circuit fault. Since an analytical solution cannot be obtained, numerical solutions are required.
[0057] In some preferred embodiments, the column integral method can be used to analyze the stability of the MCU-EME-based towing test system for inter-turn short-circuit conditions through the following steps, and to determine its safe operating boundary under the target inter-turn short-circuit parameters: S1, Establish column vectors The corresponding differential equation: (twenty two), in, This is the MCU-EME coupling coefficient matrix. for The order of , that is: pass From the order of each submatrix in the system, we can see that the total order of the system is 10.
[0058] S2, determine the target inter-turn short-circuit parameters and the electric speed analysis range, wherein the target inter-turn short-circuit parameters include the target short-circuit coefficient and the target short-circuit resistance, and the electric speed analysis range includes multiple discrete electric speed values; S3, Traverse the electric speed range, and perform steps S31 to S33 for each discrete electric speed: S31, substitute the target inter-turn short-circuit parameters and the discrete electric speed into... And solve them respectively using numerical integration methods. The differential equations are obtained. The solution corresponding to each column vector ; S32, Merge The solutions corresponding to each column vector yield the target inter-turn short-circuit parameters and the state transition matrix corresponding to the discrete electric speed. : (twenty three); S33, Calculation The corresponding eigenvalues; S4. Summarize the eigenvalues corresponding to all discrete electric speeds in the electric speed range to determine the distribution of the eigenvalues of the state transition matrix as the electric speed changes under the target inter-turn short-circuit parameters. S5. Based on the distribution of eigenvalues of the state transition matrix under the target inter-turn short-circuit parameters as a function of electric speed, determine the stability boundary of the motor simulator considering the inter-turn short-circuit motor model under the target inter-turn short-circuit parameters.
[0059] Specifically, first establish the same dimension as the system. column vectors, and substitute the coefficient matrix in equation (16) into To establish The process involves generating several differential equations, determining the target inter-turn short-circuit parameters to be analyzed, and simultaneously determining the electric speed range and step size to be analyzed, thereby obtaining multiple discrete electric speeds (for example, in the 350~500Hz range, each discrete electric speed is determined with a step size of 10Hz).
[0060] Next, it iterates through each discrete electric speed value, performing the operation of solving the differential equation for each electric speed value to determine the eigenvalues. In each solution... When solving the differential equation, the target inter-turn short-circuit parameters and discrete electric speed values will be substituted into the equation. For any number of For each differential equation, first set the initial conditions. ,in In addition to the first One element is 1, and the rest are 0. A column vector of dimension is generated, and then numerical integration methods such as the Runge-Kutta method (RK4) are used to integrate from 0 to... Integrating ( The cycle of the MCU-EME-to-trail test system for inter-turn short-circuit conditions is the time it takes for the motor to rotate one revolution, thus obtaining the first... Solutions to the differential equations traversal Solving the differential equations yields the results. One solution Then The solutions are spliced together to obtain the state transition matrix corresponding to the target inter-turn short-circuit parameters and discrete electric speed values, and the corresponding eigenvalues are determined.
[0061] After completing the above traversal operation, the eigenvalues of the target inter-turn short-circuit parameters obtained at each discrete electric speed are summarized. This allows us to determine the distribution of the eigenvalues of the state transition matrix as a function of electric speed under the target inter-turn short-circuit parameters. All eigenvalues can be plotted on the complex plane, and we can then search for eigenvalues that exceed the unit circle (i.e.,...). If the electric speed exceeds the corresponding electric speed (1), the electric speed at which the motor enters an unstable state under the target inter-turn short-circuit parameters can be determined. Obviously, this electric speed is the stability boundary of the motor simulator under the target inter-turn short-circuit parameters.
[0062] <Specific Implementation Example 1> This embodiment employs the aforementioned method for determining the safe operating boundary of a towing test system oriented towards inter-turn short-circuit conditions. It determines the system's safe operating boundary corresponding to different inter-turn short-circuit parameters and compares the results with theoretical analysis through simulation and actual measurements. The MCU control bandwidth is set to 300Hz, and the modeling error is 30%. , ).
[0063] Table 1 lists the motor model and coupling inductance parameters: Table 1 Table 2 lists the system delay parameters: Table 2 Figure 6 The figure shows the distribution of the state transition matrix characteristics of the MCU-EME-driven system with different short-circuit coefficients. Following the direction indicated by the black dashed arrows, the electric speed corresponding to the characteristic value increases from 350Hz to 500Hz, with a step size of 10Hz. Taking Figure (a) as an example, it can be seen that the electric speed corresponding to the state transition matrix characteristic value crossing the unit circle is 490Hz. Therefore, theoretically, it can be predicted that the system will become unstable at an electric speed greater than 490Hz (7350rpm).
[0064] Table 3 shows the theoretical instability boundary electric speed of the system under different short-circuit coefficients: Table 3 As shown in Table 3, when the MCU-EME simulates the inter-turn short-circuit condition of the towing system, the larger the short-circuit coefficient, the smaller the instability boundary speed of the system, and the worse the system stability.
[0065] To verify the correctness of the derived state-space equations and the effectiveness of applying Floquet theory to determine stability, such as... Figure 7 As shown, a simulation model of the MCU-EME towing test system for inter-turn short circuit conditions was built in Matlab / Simulink, and a delay module was added to the model.
[0066] The simulation time is set to 6 seconds, and an inter-turn short-circuit fault is injected at 1 second. The short-circuit coefficient is... The values are taken from 0 to 0.5, with a step size of 0.1; the MCU bandwidth is 300Hz, and the EME bandwidth depends on the feedback matrix of equation (12). The speed varies with the rotational speed; the MCU switching frequency is 10kHz, and the EME switching frequency is 50kHz. Electrical rotational speed... Set as a ramp signal, linearly increasing from 0Hz to 600Hz (9000rpm) within 6 seconds. Input d-axis reference current 0A, q-axis reference current 50A, and observe the output dq-axis current on the EME side.
[0067] Figure 8 The simulation results of the MCU-EME speed-up of the towing system under different short-circuit coefficients are shown. Taking Figure (a) as an example, when the short-circuit coefficient is 0, the d-axis current on the EME side diverges at 5.0s, and the system becomes unstable. The corresponding electric speed of the system at this time is 500Hz (7500rpm).
[0068] Table 4 shows the simplified instability boundary electric speed of the system under different short-circuit coefficients: Table 4 As can be seen, the simulation results are basically consistent with the theoretical analysis results, and the short-circuit coefficient... The larger the value, the larger the dq-axis current ripple, the smaller the threshold speed for system divergence, and the more unstable the system.
[0069] To further verify the correctness of the derived inter-turn short-circuit MCU-EME considering time delay for the drag system state space and the effectiveness of the proposed Floquet stability determination, a system was built as follows: Figure 9 The MCU-EME dual-drive experimental platform is shown. The motor model and control strategy run on the NI 9629 board, with a motor model solution step size of 2µs; the bus voltage on both the MCU and EME sides is 360V; the current acquisition and analog-to-digital conversion are processed by the AD7656 chip; the host computer uses the NI Veristand for observation, with a sampling frequency of 10kHz. The experimental conditions and parameters are consistent with the simulation.
[0070] Experimental results are as follows Figure 10As shown, to prevent excessive current from damaging the hardware when the system becomes unstable, the control program limits the current. Taking Figure (a) as an example, when the short-circuit coefficient is 0, the electric speed corresponding to the divergence of the d-axis and q-axis currents is 485Hz (7275rpm), at which point the system becomes unstable.
[0071] Table 5 shows the measured instability boundary electric speeds of the system under different short-circuit coefficients. Table 5 Plot the data from Tables 3, 4, and 5 into line charts and summarize them. Figure 11 As can be seen, the simulation and experimental results are in good agreement with the theoretical analysis results, with a maximum relative error of 5.3%; the instability boundary electric speed of the system shows a linear decreasing trend as the short-circuit coefficient increases.
[0072] The specific embodiments of this application have been described in detail above. For those skilled in the art, several improvements and modifications can be made to this application without departing from the principle of this application, and these improvements and modifications also fall within the protection scope of the claims of this application.
Claims
1. A method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model, characterized in that, include: An inter-turn short-circuit motor model is established, which includes inter-turn short-circuit parameters used to characterize the severity of inter-turn short circuits, and the transfer matrix of the inter-turn short-circuit motor model is a periodic time-varying matrix related to the inter-turn short-circuit parameters and the electrical angle of the motor. Establish a control model for the MCU-EME-to-drive test system that takes into account time delay. The EME-side control model adopts a current tracking strategy based on feedforward compensation and state feedback. The feedforward compensation voltage and the state feedback voltage are determined based on the inter-turn short-circuit motor model and the coupling inductance of the MCU-EME-to-drive test system. The MCU-EME control model and the EME control model are combined to establish a periodic time-varying state model of the MCU-EME drag test system for inter-turn short circuit conditions. The stability of the periodic time-varying state model is analyzed to determine the stability boundary of the motor simulator considering the inter-turn short-circuit motor model.
2. The method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model according to claim 1, characterized in that, The inter-turn short-circuit parameters include: Short circuit factor This indicates the proportion of the number of turns in the short-circuited winding to the total number of turns in the winding of the phase in which it is located; short-circuit resistor , which represents the equivalent resistance of the inter-turn short-circuit loop itself.
3. The method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model according to claim 2, characterized in that, The inter-turn short-circuit motor model is as follows: ， in, This represents the original dq-axis current vector of the stator winding. This is the equivalent dq-axis current vector of the motor stator winding after short-circuit current coupling correction. This is the coefficient matrix of the inter-turn short-circuit motor model. This is the input matrix for the inter-turn short-circuit motor model. Let be the back electromotive force disturbance vector caused by the permanent magnet flux linkage and the electric speed. In the inter-turn short-circuit motor model The corresponding output matrix is a 2D identity matrix. This is the dq-axis voltage vector output from the MCU side. This is the transfer matrix for the inter-turn short-circuit motor model. The electric angle of the motor.
4. The method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model according to claim 3, characterized in that, The transfer matrix for: ， in This is the stator resistance.
5. The method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model according to claim 1, characterized in that, The delay terms considered when establishing the MCU-side control model and the EME-side control model include the sampling period delay term as well as voltage amplitude and phase distortion terms.
6. The method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model according to claim 3, characterized in that, The MCU-side control model considering delay is established based on an internal model decoupling control strategy, and its state-space equation is: ， in, The input command current vector is provided on the MCU side. The coefficient matrix of the MCU-side control model. In the MCU-side control model The corresponding input matrix For the MCU-side control model The corresponding input matrix, The output matrix of the MCU-side control model. This is the state vector of the internal model decoupling controller on the MCU side.
7. The method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model according to claim 6, characterized in that, The state-space equation of the EME-side control model considering time delay is: ， in, This is the coefficient matrix of the coupled inductor model. This is the phase distortion matrix caused by EME-side delay. In the coupled inductor model The corresponding input matrix, In the coupled inductor model The corresponding input matrix, The output voltage vector on the EME side; , , This is the intermediate matrix determined by the current tracking strategy based on feedforward compensation and state feedback. This is the autonomous term matrix with delay on the EME side. Let dq be the current vector of the coupled inductor. This is the internal state vector of the EME-side controller.
8. The method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model according to claim 7, characterized in that, The periodic time-varying state model of the MCU-EME drag test system for inter-turn short-circuit conditions is as follows: ， in, , This is the MCU-EME coupling coefficient matrix.
9. The method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model according to claim 8, characterized in that, The MCU-EME coupling coefficient matrix for: 。 10. The method for determining the stability boundary of a motor simulator considering an inter-turn short-circuit motor model according to claim 7, characterized in that, The stability analysis of the periodic time-varying state model includes the following steps: S1, Establish column vectors The corresponding differential equation: ， in, This is the MCU-EME coupling coefficient matrix. for The order of; S2, determine the target inter-turn short-circuit parameters and the electric speed analysis range, wherein the target inter-turn short-circuit parameters include the target short-circuit coefficient and the target short-circuit resistance, and the electric speed analysis range includes multiple discrete electric speed values; S3, Traverse the electric speed range, and perform steps S31 to S33 for each discrete electric speed: S31, substitute the target inter-turn short-circuit parameters and the discrete electric speed into... And solve them respectively using numerical integration methods. The differential equations are obtained as follows: The solution corresponding to each column vector ; S32, Merge The solutions corresponding to each column vector yield the target inter-turn short-circuit parameters and the state transition matrix corresponding to the discrete electric speed. : ； S33, Calculation The corresponding eigenvalues; S4. Summarize the eigenvalues corresponding to all discrete electric speeds in the electric speed range to determine the distribution of the eigenvalues of the state transition matrix under the target inter-turn short-circuit parameters as the electric speed changes. S5. Based on the distribution of eigenvalues of the state transition matrix under the target inter-turn short-circuit parameters as a function of electric speed, determine the stability boundary of the motor simulator considering the inter-turn short-circuit motor model under the target inter-turn short-circuit parameters.