## 3 Five-Phase Induction Motor Control
### Basic Control Scheme Used in Normal Operation during the Measurement  
The measurement in normal operation was performed using the scheme of the field-oriented control presented in Figure 5 to compare the machine in normal operation and a one-phase fault operation. The same control method was employed without any intervention in the control for the measurement of the motor with one phase defect. Figure 4: Graphical representation of the phase current adjustment during operation of a five-phase open-phase induction motor. The field-oriented control is well known from three-phase motors. The difference in the five-phase vector control is only in the use of five-phase Clarke and Park transformations, as well as five-phase inverse transformations. In the diagram in Figure 5, the \(i_{a}\)-\(i_{e}\) currents flowing through the motor are measured. The symbol \(\omega\) represents the angular velocity of the rotor of a five-phase induction motor, \(\theta\) represents the rotor flux position. \(DM\) represents a dynamometer, VSI is a voltage source inverter. The PI block displays the proportional integration controller [36, 37]. Design of an Algorithm for Adjusting the Control during a Single-Phase Failure to Improve Motor Characteristics  
One of the most important aspects that is heavily emphasized is the safety of electric drive in EV and HEV. If the drive fails and the machine is unable to continue operating during traffic, the results could be disastrous. As a result, new driving methods and controls are being implemented to eliminate this risk. As previously stated, one option is to use a multiphase motor, which provides better fault tolerance. Figure 6 depicts a new control method that ensures normal operation in the event of a phase failure. The original vector control scheme no longer includes the PI current controllers for \(i_{d}\) and \(i_{q}\), as well as the Park and Clarke transformation. Only the components of the currents \(i_{a}\) and \(i_{\beta}\) are active in the fault-free sinusoidal balanced motor. Components x, y, and 0 are all zero. However, if a phase failure occurs and the MMF is no longer sinusoidal, the situation changes. The motor power decreases as it begins to produce a large ripple torque. The components of the currents x, y, and 0 are also active in this case, and the components of the currents \(i_{x}\) and \(i_{y}\) are used to eliminate the fault state. From the control scheme in Figure 6, by a suitable recalculation of the components of the currents \(i_{x}\) and \(i_{y}\) using the currents \(i_{a}\) and \(i_{\beta}\), we can provide again the sinusoidal MMF. In the new control scheme, all required currents from the transformation are then compared with the measured currents and regulated in the PI controllers. Figure 5: Scheme of vector control of a five-phase induction machine. Figure 6: The fault-tolerant control scheme for a five-phase induction machine. The calculation of the constants K1-K4, which provide again sinusoidal MMF, is given by the solution of the current matrix (39). It has to be considered that in the error phase, the current is zero. In our case, \(i_{a}=0\). \[\left[ \begin{array}{c}i_{a}\\ i_{\beta}\\ i_{x}\\ i_{y}\\ i_{0}\end{array} \right]=\frac{2}{5}\left[ \begin{array}{ccc}1&cos\big{(} \frac{2\pi}{5}\big{)}&cos\Big{(}\frac{4\pi}{5}\big{)}&cos\big{(}\frac{6\pi}{5} \big{)}&cos\big{(}\frac{8\pi}{5}\big{)}\\ 0&-sin\big{(}\frac{2\pi}{5}\big{)}&-sin\big{(}\frac{4\pi}{5}\big{)}&-sin\big{(} \frac{6\pi}{5}\big{)}&-sin\big{(}\frac{8\pi}{5}\big{)}\\ 1&cos\big{(}\frac{6\pi}{5}\big{)}&cos\big{(}\frac{12\pi}{5}\big{)}&cos\big{(} \frac{18\pi}{5}\big{)}&cos\big{(}\frac{24\pi}{5}\big{)}\\ 0&-sin\big{(}\frac{6\pi}{5}\big{)}&-sin\big{(}\frac{12\pi}{5}\big{)}&-sin\big{(} \frac{18\pi}{5}\big{)}&-sin\big{(}\frac{24\pi}{5}\big{)}\\ \frac{1}{2}&\frac{1}{2}&\frac{1}{2}&\frac{1}{2}&\frac{1}{2}\\ \end{array} \right]\left[ \begin{array}{c}i_{a}\\ i_{b}\\ i_{c}\\ i_{d}\\ i_{e}\end{array} \right].