Optimizing Control Strategy of Electric Motors with MTPA

Introduction

Maximum torque per ampere (MTPA) is an optimization strategy for the control of electric motors and drives that employ field-oriented control (FOC), particularly with electric vehicles (EVs) and industrial automation applications. The goal of MTPA is to achieve the maximum possible torque output from a motor for a given current input. The maximum torque value corresponds to specific current magnitudes and can be decomposed into its quadrature and direct axis components. These data points are then organized into an MTPA curve or table and implemented into a drive control system to optimize efficiency of the motor under various operating conditions.
 

Using FOC to get MTPA

FOC is a widely adopted method for controlling electric motors, especially synchronous machines like permanent magnet synchronous motors (PMSM) and brushless DC motors (BLDC). It enables precise control of the motor's magnetic field and torque by decoupling the stator current into two orthogonal components – the direct axis (d-axis) and the quadrature axis (q-axis). The d-axis current component (Id) controls the magnetic field, while the q-axis current component (Iq) controls the torque.

MTPA directly relates to FOC by optimizing the distribution of the current components to maximize torque output for a current magnitude. MTPA ensures efficient motor operation, generates the highest possible torque without exceeding current limits, and allows the motor to run at an optimal combination of Id and Iq to achieve higher torque for the same stator current.
 

What is the MTPA Curve?

A maximum torque test determines optimal operating points, which are then graphed in an MTPA curve or tabulated for integration into a motor controller. The MTPA curve shows the optimal combination of Id and Iq that maximizes torque per unit of current and minimizes stator current losses to enhance efficiency. An MTPA graph may contrast the MTPA curve with a constant torque curve, which represents the points where the motor maintains steady torque output regardless of speed. While the constant torque curve focuses on maintaining torque, the MTPA curve aims to achieve the highest torque with the least current for better motor performance.
 

Curve Generation

The MTPA curve is generated through a series of tests and measurements that map out optimal Id and Iq values at various torque demands. This process begins with varying Id and Iq within safe operating limits and recording the corresponding torque output. This data (i.e., current magnitude, torque, quadrature currents, direct currents) is collected across a range of operating conditions of speed and torque to ensure a comprehensive dataset that covers the full operational envelope of the motor.

The collected data enables users to determine torque per ampere (TPA) values. Next, they select the highest TPA values and identify the corresponding Id and Iq values to construct the MTPA curve for each step in total current magnitude. Finally, this MTPA curve is implemented into the motor control algorithm with continuous monitoring control each parameter ensuring optimal motor performance at all conditions.
 

MTPA Testing & Validation

MTPA testing and validation requires a motor drive setup (typically a PWM drive and PMSM motor) that implements a FOC scheme, plus a power analyzer capable of accurate AC power measurements on high-current signals and mathematical computations on the captured data. Instructions and data in this application note are provided using a Yokogawa Test&Measurement WT5000 Precision Power Analyzer.

In this example, a motor test stand is set up with a PMSM loaded by a hysteresis brake. The motor is in torque control while the brake provides speed control. The motor drive is programmed to output a constant current magnitude and sweep through Id and Iq values that match the total magnitude. Once the entire range for a current magnitude and speed is run through, the values are varied to cover the motor’s full operating spectrum.
 

Figure 1. Schematic of motor and dynamometer
 

The power analyzer measures power on the motor drive’s three-phase AC signal. Torque, speed, and position sensors are also employed to calculate mechanical power. With the position value and current magnitude, the power analyzer calculates quadrature and direct current values.
 

Figure 2. MTPA calculation formulas
 

Figure 3. Implementing the equations
 

Next, a sweep output of the data points is recorded for analysis of maximum TPA value and its corresponding Id and Iq values.

Figure 4. Measuring sweep of Id and Iq
 

The max TPA value for each step in current magnitude and its Id and Iq values are identified and the data points generate the table and curve for implementation into the motor controller.

The data can also be articulated into a table or graphical curve, as seen in Figures 5 and 6.

Figure 5. MTPA data table

Figure 6. MTPA curve
 

After the data points are collected, this optimization can be integrated into the motor drive's control algorithm and the motor drive can refer to this optimization table during various loads in its operation.
 

Conclusion

MTPA is a fundamental strategy in electric motor control that leverages the principles of FOC to optimize torque output for a given current. By carefully mapping and implementing the MTPA curve, users can significantly enhance efficiency, performance, and longevity of electric motors across various applications. Whether used with EVs, industrial automation, renewable energy systems, or home appliances, MTPA enables motor control technology advancements and innovations.