For permanent magnet synchronous motor drive systems, the safe state is generally either shut-off or active short circuit (ASC).
Because permanent magnet synchronous motors (PMSMs) have back electromotive force (EMF), shutting off the motor at high speeds could generate excessive torque, violating safety requirements. Therefore, high-speed PSMs are designed with an active short circuit as a safety feature. This active short circuit involves deliberately short-circuiting the three phases of the motor. After entering a steady state through this active short circuit, the output torque of the PMSM in the medium-to-high speed range is approximately zero, meeting torque safety requirements.
Today, as a beginner in electrical control, I'll be discussing the dynamic current changes when a motor directly enters an active short circuit.
A Brief Analysis of Steady-State Current in High-Speed ASC
Let's first briefly analyze the current situation of a permanent magnet synchronous motor after it enters ASC at high speed. To analyze this problem, even a novice in electrical control will need to use the DQ axis voltage equation of a permanent magnet synchronous motor, which is indispensable:
To analyze the steady-state current, the equations are simplified to steady-state equations:
An active short circuit short-circuit connects the three phases of the motor, so both ud and uq are 0. The steady-state current can then be derived.
As can be seen from the expression, the steady-state current of the D-axis is less than 0. The steady-state current of the Q-axis has the opposite sign to the speed. When the motor is running in the medium-to-high speed range, the inductive reactance of the D and Q axes will be much greater than Rs, and the Q-axis current will be approximately 0. Therefore, the motor is operating in a low-power (high-speed, low-torque) generating state.
The reason why a motor must be in a low-torque generating state is actually easy to understand: when the three phases of the motor are short-circuited, the motor cannot exchange energy with the DC terminal. However, as long as there is current in the three phases of the motor, there will inevitably be energy consumption (copper loss and iron loss). This part of the energy can only be converted from external kinetic energy. Therefore, the motor must be in a generating state, and the generating power will not be too large (the generating power must be equal to the motor's loss power).
Ignoring the Rs-related terms, we obtain an approximate expression for the current:
Therefore, for high-speed ASC, the steady-state current of the permanent magnet synchronous motor is actually approximately equal to the characteristic current i0 of the motor.
Dynamic current analysis of entering ASC from electric state
Next, we will continue to analyze the dynamic process after the motor enters ASC:
For ease of analysis, let's define the operating states first: forward rotation, electric operation, id>i0
When the motor transitions from normal operating state to ASC, the motor terminal voltage becomes 0:
From the expression above, we can see that when iq > 0, id increases; when iq < 0, id decreases. When id > i0, iq decreases; when id > i0, iq decreases.
To verify the accuracy of the previously discussed complex dynamic analysis, this novice in electrical control used a Matlab simulation model (please forgive my limited resources; I couldn't use actual bench test data). The simulation waveforms are shown below:
As can be seen from the waveform above, the dynamic change process of the DQ axis current is basically consistent with the previous analysis by the novice in electrical control. This shows that the previous analysis method is correct (thankfully, it is consistent, otherwise it would be a slap in the face).
We can also draw the following conclusions from the waveform:
1. When a motor transitions directly from normal operation to ASC (Automatic Selective Control), a large current surge may occur. This surge current is primarily caused by the D-axis current, and it occurs slightly before the motor switches from generator mode to motor mode.
2. The impact amplitude of the D-axis current may be much larger than the steady-state current (the D-axis current impact reached 1450A in the simulation waveform);
3. Switching to ASCII will cause the DQ axis current to oscillate;
4. The amplitude of the current oscillation caused by switching to ASC will gradually decrease, and eventually the current will converge to the steady-state current value. The waveform of the DQ axis current is the steady-state value superimposed with the oscillating current whose amplitude gradually decreases.
5. The oscillation component in the Q-axis current leads the oscillation component of the D-axis current by approximately 90° (less than 90°) in phase.
Tips:
1. Simulation conditions: The motor operates at a frequency of 200Hz. Before entering ASC, the motor's Id = -200A and Iq = 400A. The steady-state voltage Id under high-speed active short circuit is approximately -600A.
2. The oscillation frequency of the DQ axis current is the same as the electrical frequency of the motor, both being 200Hz;
3. Why is the inrush current mainly formed by the D-axis current? Because the D and Q-axis currents are orthogonal, and the magnitude of the current vector is the sum of the squares of the D and Q-axis currents. Also, when the D-axis current reaches its peak, the Q-axis current is approximately zero. Therefore, the influence of the Q-axis current on the current magnitude at this point can be ignored.
4. Why doesn't the maximum value of the D-axis current correspond to the moment when the Q-axis current is 0, as analyzed earlier? This is because the influence of the stator resistance Rs was ignored in the previous analysis. If the influence of Rs is introduced, the analysis results will correspond to the waveform. I won't elaborate further here, as I'm a novice in electrical control; interested readers can analyze it themselves.
5. Why does the oscillating component in the current gradually decay to 0? Because of the stator resistance, which consumes the energy of the oscillation, causing the current to gradually converge. Alternatively, the resistor and inductor form a first-order low-pass filter, which attenuates the AC signal, thus eventually reducing the AC component to 0.
6. Why does the maximum inrush current always occur slightly before the motor transitions from generator to motor? This can be understood from an energy perspective. The larger the DQ axis current, the more energy the motor inductor stores. After the motor enters ASC state, energy can only interact with mechanical energy. In motoring state, the inductor magnetic field energy is converted into mechanical energy, and the inductor current decreases. In generator state, mechanical energy is converted into inductor magnetic field energy, and the inductor current increases. Therefore, the current amplitude in generator state is always greater than that in motoring state. At the same time, the motor itself has losses (copper losses and iron losses). Therefore, when the generator power equals the motor's own losses, the inductor energy reaches its maximum, and the corresponding current reaches its maximum.
Dynamic current analysis of ASC during power generation
Having analyzed the dynamic current change process when switching from the generating state to ASC, we will now analyze the dynamic current change process when switching from the generating state to ASC, again using the previous formula:
Even beginners in electrical control can use simulation to verify the correctness of their analysis:
As can be seen from the waveform above, the dynamic change process of the DQ axis current is basically consistent with the previous analysis by the electronics novice, which shows that the previous analysis method is correct.
We can draw the same conclusions from the waveform as we do from the electric operating condition. I won't go on and on about the electric control system here, so as not to waste your precious time.
Comparing the waveforms of electric and generator states, it is not difficult to find that the electric state eventually enters the same current change process as the generator state. The electric state only adds a transition process to generator state, but it has no impact on the operating point where the maximum inrush current occurs.
DQ axis dynamic current oscillation component amplitude relationship
Let's first analyze the amplitude relationship of the DQ axis oscillation components. Let's define the variables we need to use in the analysis first, so that you don't get confused later.
i0—Motor characteristic current
idm—Amplitude of D-axis current oscillation component
iqm—Amplitude of Q-axis current oscillation component
Based on the preceding analysis, both electric and electric power generation will eventually enter the power generation mode. Therefore, we will directly analyze the power generation mode here. To simplify the analysis, we will not consider the attenuation effect of resistance on the oscillation, that is, we will assume that the oscillation amplitude is constant.
By appropriately modifying the formula used in the previous analysis of dynamic changes in current:
The waveform between T1 and T2 in the above waveform corresponds exactly to one-quarter of the period of the DQ axis oscillation component; therefore, the change in the D-axis current from time T1 to time T2 is exactly the amplitude Idm of the resonant component; at the same time, the definite integral of iq from T1 to T2 is the area of the green shaded region in the figure, and the integral value of iq can be calculated using the definite integral formula:
From the corresponding relationship of the DQ axis oscillation current amplitude, it can be seen that for a built-in salient pole motor (Ld
Calculation of D-axis current oscillation component amplitude
I'm sure you won't be satisfied with just analyzing the relationship between the amplitudes of the D and Q axis oscillation currents. So, for those new to electrical control, let's analyze the maximum amplitude of the D-axis current. We'll also directly analyze the power generation condition.
We'll still use the definite integral formula from before, but this time we'll be performing a definite integral over the time interval from T0 to T1, assuming the time interval from T0 to T1 is t:
The change in the D-axis current is (i0-id0); the definite integral of iq is the negative of the area of the red shaded region in the figure. For ease of calculation, we approximate the red shaded area with the area of the trapezoid ACFG.
The change in Q-axis current is (-iqm-iq0); the definite integral of (i0-id) is the opposite of the area of the green shaded region in the figure. Similarly, for ease of calculation, we use the area of triangle BDE to approximate the equivalent green shaded area.
As can be seen from the formula for the magnitude of the D-axis impact current, the magnitude of the current impact is not only related to the parameters of the motor itself, but also to the initial value of the current at the moment of entering ASC.
Tips:
1. The above analysis is conducted under the condition of neglecting the influence of stator resistance Rs. Therefore, the analysis here is on the maximum value of the oscillating current under the condition of no attenuation.
2. In reality, due to the attenuation effect of Rs, the amplitude of the current surge is generally smaller than the value analyzed here.
Summarize
This presentation mainly analyzes the dynamic change of current when a permanent magnet synchronous motor directly enters ASC (Automatic Stability Control) mode from normal operating conditions at high speed.
1. After the motor enters ASC mode, an oscillating current will be generated on the DQ axis. The frequency of the oscillating current is the same as the motor's operating frequency.
2. Due to the presence of stator resistance, the oscillating current will gradually decrease, and the DQ axis current will eventually converge to the ASC steady-state current;
3. After the permanent magnet synchronous motor enters ASC (Automatic Current Scheme), the steady-state operating current is basically equal to the characteristic current of the motor, and the motor is in a low-power generation state;
4. Regardless of the operating condition from which the motor enters ASC, it will eventually enter the same convergence condition, with the maximum inrush current caused by the D-axis current;
5. The maximum value of the inrush current depends not only on the parameters of the motor itself, but also on the initial value of the current at the moment of entering ASC.
That concludes today's sharing. I hope this sharing from an electrical control novice will help you understand the dynamic current process of the ASC motor in a permanent magnet synchronous motor.
