Hi @mamad ,
After going through documentation provided at the link below
https://www.mathworks.com/discovery/field-weakening-control.html
It is my understanding that Flux weakening control, also known as field-weakening control, involves manipulating the magnetic field within an electric motor to allow it to operate at speeds exceeding its nominal rating. This is achieved by reducing the magnetic flux produced by the rotor, which allows the motor to maintain higher speeds while keeping power output constant.
In Permanent Magnet Synchronous Motors (PMSMs), this technique is often utilized because PMSMs are known for their high power density and dynamic response. The basic principle involves regulating the d-axis and q-axis currents to achieve the desired speed without exceeding voltage limits.
Understanding Flux Weakening Control
Field-weakening control operates by manipulating the d-axis and q-axis currents in the motor to reduce the magnetic flux produced by the rotor's permanent magnets. This reduction allows the motor to achieve higher speeds while maintaining a constant output power, which is the product of torque and speed. The key to successful implementation lies in understanding the torque-speed characteristic curve and the constraints imposed by the motor's voltage and current limits.
Maximum Current Calculation
The maximum current in a PMSM during flux weakening can be calculated based on the voltage constraints and the motor's operational characteristics. The relationship can be expressed as follows:
1. Voltage Limit: The maximum voltage ( V_{max} ) is determined by the DC bus voltage and the inverter's output capabilities.
2. Current Limit: The maximum current ( I_{max} ) can be derived from the voltage equation: [ V = L \frac{di}{dt} + R i + E_{emf} ] where ( L ) is the inductance, ( R ) is the resistance, and ( E_{emf} ) is the back electromotive force.
3. Field Weakening Region: In the field-weakening region, the d-axis current ( i_d ) is driven negative, which reduces the effective flux linkage. The q-axis current ( i_q ) is adjusted to maintain the desired torque.
Below is a MATLAB code snippet that simulates the flux weakening control of a PMSM. This code includes the calculation of maximum current and generates a plot of the current trajectories.
% Parameters V_dc = 600; % DC bus voltage in volts R = 0.5; % Resistance in ohms L = 0.01; % Inductance in henries omega = linspace(0, 4000, 100); % Speed in RPM E_emf = 0.1 * omega; % Back EMF proportional to speed
% Calculate maximum current I_max = (V_dc - E_emf) / R; % Maximum current calculation
% Plotting the results
figure;
plot(omega, I_max, 'LineWidth', 2);
title('Maximum Current vs. Speed in PMSM');
xlabel('Speed (RPM)');
ylabel('Maximum Current (A)');
grid on;
legend('I_{max}');
Final Plot
The above code will generate a plot illustrating the relationship between the motor speed and the maximum current. The plot will show how the maximum current decreases as the speed increases, reflecting the constraints imposed by the back EMF and resistance.
Please see attached.
Please refer to this example provided in Simulink to help you get started with a project if you are interested.
https://www.mathworks.com/help/sps/ug/pmsm-field-weakening-control.html
Hope this helps.
Please let me know if you have any further questions.
