The permanent magnet synchronous machine is considered one of the significant electric machines used in different applications due to its high torque density, high power density, high efficiency, and low maintenance. Due to the PM synchronous machines' design, the control system can drive the motor to deliver high torque to mechanical loads with the lowest current, which is called the maximum torque per ampere (MTPA) control method, and operate the generator to inject maximum electric energy into the grid at any mechanical power, which is called the maximum power extraction (MPE).

MTPA control can be achieved by direct voltage control. Therefore, a simple direct voltage MTPA control strategy is suggested with a thorough insight analysis to define the control gains analytically, which simplifies the control ultimately and makes it more suitable for low-cost real-time implementation compared to other methods. The proposed method tracks the MTPA trajectory by finding the optimal pair of voltage angle and amplitude for each motor's speed and torque conditions. This is achieved without the need for any current control loop, which makes the technology simple to a great extent, contrary to most methodologies, but this simplicity is made possible by ignoring transient terms that guarantee MTPA only at steady-state. To overcome this limitation, simple dynamic direct control approaches are proposed to compensate for transient terms, making MTPA operation possible in all operating conditions with/without current sensors. The proposed strategies are applied to an interior permanent magnet synchronous motor (IPMSM) for industrial and electric vehicle applications and a surface-mount permanent magnet synchronous generator (SPMSG) for wind energy conversion system implementations.

To illustrate the suggested control methods' capability, comparative studies are conducted against the popular MTPA vector control strategy. Experimental results for various situations reveal the suggested MTPA controllers' ability. Additionally, to quantitatively assess the MTPA trajectory tracking accuracy, the proposed control methods are compared using a qualification metric with energy consumption and energy efficiency studies.