⚡ electrical engineering

Flux-map-based optimal current reference generation for copper-loss minimization and fault-tolerant control of a six-phase electrically excited synchronous motor

This paper proposes and experimentally validates a variable-field look-up-table strategy for six-phase electrically excited synchronous motors that utilizes nonlinear flux-linkage maps to generate optimal current references, thereby significantly minimizing copper losses and ensuring fault-tolerant operation under single open-phase faults.

Original authors: Mohamed Ahmed Osman, Ayman Samy Abdel-Khalik, Ragi Ali Hamdy, Abdelrahman Ismail

Published 2026-10-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Mohamed Ahmed Osman, Ayman Samy Abdel-Khalik, Ragi Ali Hamdy, Abdelrahman Ismail

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Electric motors are the silent workhorses of modern life, powering everything from factory robots to the cars we drive. For decades, the most powerful and efficient versions of these machines have relied on permanent magnets, chunks of rare metal that create a constant magnetic field without needing electricity. However, these magnets depend on materials that are difficult to source and environmentally costly to extract. This has pushed engineers to look for alternatives, specifically motors that create their own magnetic fields using coils of wire and electricity, much like an electromagnet. These machines offer a unique advantage: because the magnetic field is created by electricity, it can be adjusted on the fly. This flexibility allows the motor to adapt to different speeds and loads more effectively than its permanent magnet cousins. Yet, this very flexibility creates a complex puzzle. Since the motor has multiple ways to generate the same amount of power by mixing different amounts of current in different parts of the machine, finding the single best combination to save energy is incredibly difficult, especially when the machine is pushed to its limits or when a part of it breaks.

A team of researchers at Alexandria University and Sultan Qaboos University has tackled this puzzle by developing a new way to control a specific type of six-phase electric motor. This motor is designed with six separate sets of wires instead of the usual three, a design that makes it more reliable and capable of running even if one of the wires fails. The researchers focused on a machine that uses an electrically excited rotor, meaning it generates its magnetic field through a separate coil rather than permanent magnets. The core challenge they addressed was how to decide exactly how much electricity to send to the main motor coils and how much to the rotor coil at any given moment. If the wrong amounts are chosen, the motor wastes energy as heat, a problem known as copper loss. While older methods could find a good setting, they often missed the absolute best one because they treated the motor's internal magnetic behavior as simple and unchanging, ignoring the fact that the metal inside the motor becomes magnetically "full" or saturated when pushed hard.

To solve this, the researchers created a sophisticated digital map of the motor's behavior. Instead of guessing how the motor reacts, they physically tested the machine, running it through thousands of different combinations of speed, torque, and electrical current. They measured the results to build a detailed, three-dimensional picture of how the magnetic fields inside the machine actually behave under real-world conditions, including the complex effects of magnetic saturation. Using this experimental data, they ran an optimization process on a computer to find the perfect mix of currents that would produce the required power while wasting the least amount of energy as heat. They stored these perfect settings in a look-up table, a pre-calculated guide that the motor controller can consult instantly. This guide tells the motor exactly how much current to send to the main windings and how much to the rotor field winding for every possible speed and load, ensuring the machine always operates at its most efficient point.

The team tested this new control strategy on a physical prototype of the motor, comparing it against two other common methods: a standard control technique that keeps the rotor field constant, and a more traditional method that does not optimize for total energy loss. The results were clear. When the motor was running normally, the new strategy reduced the total energy wasted as heat by an average of 8.57 watts compared to the standard method, and by 21.9 watts compared to the constant-field method. Over a wide range of healthy operating points, the savings were significant, with a maximum reduction of 27 watts, which represents a 37 percent improvement in efficiency relative to the standard method. The researchers also tested the system under a fault condition, simulating a scenario where one of the six power lines to the motor was cut. Even with this damage, the new control strategy allowed the motor to continue running smoothly, redistributing the electrical load to the remaining wires to maintain stable speed and power. In this damaged state, the new method reduced the total energy loss by more than half compared to the standard approach.

This work demonstrates that by carefully mapping the real-world behavior of a motor and using that data to pre-calculate the most efficient settings, engineers can significantly improve the performance of electric drives. The approach is particularly valuable for electric vehicles and other applications where every watt of saved energy extends the range of the battery and reduces the heat that the cooling systems must manage. By proving that the motor can also handle a broken wire without stopping, the study highlights a path toward machines that are not only more efficient but also more robust and reliable. The researchers confirmed their findings through rigorous physical testing, showing that the theoretical savings translate directly into real-world performance gains, offering a practical solution for the next generation of electric transportation and industrial machinery.

Technical Summary: Flux-Map-Based Optimal Current Reference Generation for Six-Phase EESM

Problem Statement
Electrically Excited Synchronous Motors (EESMs) offer a distinct advantage over Permanent Magnet Synchronous Motors (PMSMs) by utilizing rotor field windings, thereby eliminating reliance on rare-earth materials and providing an additional degree of freedom through independent rotor-field current control. However, this flexibility introduces a complex control challenge: multiple combinations of stator $d$ – $q$ currents ( $i_d, i_q$ ) and rotor field current ( $i_f$ ) can produce the same electromagnetic torque. Selecting the optimal combination to minimize total copper losses is complicated by magnetic saturation, which renders machine parameters nonlinear and current-dependent.

While Maximum Torque Per Ampere (MTPA) strategies are standard for PMSMs, they often neglect rotor field losses when applied to EESMs. Furthermore, existing optimization methods for EESMs often rely on analytical solutions that require iterative calculations or assume constant inductances, failing to fully capture magnetic saturation effects. Additionally, while multiphase machines offer inherent fault tolerance, integrating copper-loss-optimized control with fault-tolerant capabilities in six-phase EESMs remains an under-explored area, particularly regarding the interaction between primary and secondary subspaces during open-phase faults.

Methodology
The paper proposes a Flux-Map-Based Variable-Field Look-Up Table (VF-LUT) strategy to generate optimal current references for a six-phase EESM. The methodology is structured as follows:

Experimental Characterization: Instead of relying on analytical models with constant parameters, the authors experimentally obtained three-dimensional nonlinear flux-linkage maps ( $\phi_d, \phi_q$ ) as functions of $i_d$ , $i_q$ , and $i_f$ . This was achieved by sweeping currents across the operating range at specific field current levels (0.5 A, 0.75 A, and 1 A) to capture magnetic saturation effects accurately.
Offline Optimization: An offline constrained optimization problem was formulated to minimize the Minimum Total Copper Loss (MTCL) objective function, defined as $P_{cu} = 3R_s(i_d^2 + i_q^2) + R_f i_f^2$ $P_{c u} = 3 R_{s} (i_{d}^{2} + i_{q}^{2}) + R_{f} i_{f}^{2}$ . The optimization was solved over the full torque–speed envelope (0–3000 rpm, 0–7 N·m) subject to:
- Torque production constraints.
- Stator current limits (rated 7 A).
- Stator voltage limits (derated to 90% of rated voltage to reserve headroom for post-fault secondary subspace control).
- Field current bounds (0.5 A to 1 A).
  The optimization utilized a multi-start Sequential Quadratic Programming (SQP) algorithm with trilinear interpolation of the experimental flux maps.
Control Architecture: The resulting optimal current references ( $i_d^*, i_q^*, i_f^*$ $i_{d}^{*}, i_{q}^{*}, i_{f}^{*}$ ) are stored in a VF-LUT. During real-time operation, the controller retrieves these references based on the operating torque and speed.
- Healthy Operation: Secondary subspace currents ( $i_x, i_y$ ) are set to zero.
- Fault-Tolerant Operation (1OPF): Under a single open-phase fault, the secondary subspace currents are algebraically determined from the fundamental subspace currents to maintain torque production and balance the remaining phases, without requiring additional independent optimization variables.

Key Contributions
The paper identifies four primary contributions:

VF-LUT Generation: Development of a variable-field look-up table for a six-phase EESM where $i_d$ , $i_q$ , and $i_f$ are simultaneously optimized offline to minimize combined stator and rotor copper losses.
Incorporation of Saturation: The use of experimentally obtained 3D flux-linkage maps to account for magnetic saturation across the entire torque–speed range, avoiding the inaccuracies of constant inductance approximations.
Fault-Tolerant Integration: Evaluation of the healthy-optimized VF-LUT under single open-phase fault (1OPF) conditions, demonstrating that the strategy maintains stable operation by redistributing currents in the secondary subspace based on MTPA criteria.
Comprehensive Experimental Validation: A rigorous comparison of the proposed VF-LUT against conventional Field-Oriented Control (FOC) and a Constant-Field Look-Up Table (CF-LUT) under both healthy and 1OPF conditions, including dynamic performance and loss analysis.

Results
Experimental validation was conducted on a 1.1 kW, six-phase EESM test bench using a dSPACE platform. The results demonstrate:

Healthy Operation: Across 17 matched operating points, the VF-LUT reduced total copper loss by an average of 21.9 W compared to the CF-LUT and 8.57 W compared to conventional FOC. The maximum reduction observed was 27 W (37%) relative to FOC, primarily occurring at low and medium load conditions where field current optimization significantly reduces rotor losses.
Dynamic Performance: In dynamic torque-speed profile tests, the VF-LUT reduced accumulated total copper-loss energy from 5.5782 kJ (FOC) to 3.8127 kJ, a 31.65% reduction, while maintaining stable speed and current tracking.
Fault-Tolerant Operation (1OPF): Under single open-phase fault conditions, the VF-LUT maintained stable speed and torque regulation. The accumulated total copper-loss energy (including secondary subspace contributions) decreased from 4.2658 kJ (FOC) to 2.0037 kJ, representing a 53.03% reduction.

Significance and Claims
The authors claim that the proposed VF-LUT strategy effectively addresses the trade-off between efficiency and fault tolerance in six-phase EESMs. By leveraging experimental flux maps, the method achieves superior copper-loss minimization compared to both conventional FOC and constant-field optimization approaches. The study confirms that optimizing the field current alongside stator currents is critical for efficiency, particularly in partial-load regions. Furthermore, the paper demonstrates that this efficiency-optimized control strategy does not compromise fault tolerance; the system can successfully transition to 1OPF operation with significant energy savings retained, validating the approach for safety-critical applications such as electric vehicles and aerospace systems where reliability and efficiency are paramount.

Technical Summary: Flux-Map-Based Optimal Current Reference Generation for Six-Phase EESM

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