32 There is also the challenge of hybrid vehicles and hybrid transmissions that have clutches, transients, multiple machines and changing states, creating currents that are constantly changing in terms of amplitude and frequency. Transients will impact the vehicle durability (gearboxes, transmissions, etc), performance and user experience creating a demand for accurate measurements of powertrain dynamics. Torque measurement in vehicles is also a challenge because the driveshaft is often hard to access or alter. Testing this is possible with custom sensors, telemetry systems and estimation models or using a strain gauge on the shaft. Maximum torque per ampere (MTPA) is an optimisation strategy for the control of electric motors in EVs using field-oriented control (FOC). The goal of MTPA is to achieve the maximum possible torque output from a motor for a given current input. The maximum torque value, which corresponds to specific current magnitudes, can be decomposed into its quadrature and direct axis components. These data points are then organised into an MTPA curve or table and implemented into a drive control system to optimise motor efficiency under various operating conditions. Using FOC to get MTPA FOC is a widely adopted method for controlling electric motors, especially synchronous machines such as permanent magnet synchronous motors (PMSMs). 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 optimising the distribution of the current components to maximise 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. The MTPA curve A maximum torque test determines optimal operating points, creating an MTPA curve or tabulation for integration into a motor controller. The MTPA curve shows the optimal combination of Id and Iq that maximises torque per unit current and minimises 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 by varying Id and Iq within safe operating limits and recording the corresponding torque output. These data (i.e., current magnitude, torque, quadrature currents and direct currents) are 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. Tech focus | Motor testing January/February 2026 | E-Mobility Engineering Testing is possible with custom sensors, telemetry systems and estimation models or using a strain gauge on the shaft Measuring the sweep of the MTPA curve (Image: Yokogawa)
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